I think there can be ways that single-character TB can be made interesting, but it'd take a lot of thinking outside of the box. I think I would start out by thinking about emulating the resources of multiple characters into one character with multiple resources. Positioning of course you can't do much about. But outside of positioning, you can try to "represent" as much of multiple characters as possible with one character. Probably too late for AOD but it's been on my mind.
I've been thinking about that myself for some time, though my conclusions on the topic probably wouldn't sway popular opinion around here. Generally combat, tb or otherwise, seems to boil down to resource management; making your opponents waste resources while keeping your own economy safe, or at the very least making sure to stay ahead in terms of expended resources per turn. In the most basic scenario you'd just be standing there, taking turns in whacking each other until whichever one joined the battle with the biggest gun, that is stats, skills and equipment, is declared victor and goes on his merry way. Sometimes there are various trade-offs to be considered, like for instance a stun ability that does less damage, which is a fairly generic defensive measure, or an aimed shot, which is a gamble between doing overall more damage p. ap and missing your intended target entirely -- y'know, stuff like that -- but for the most part we just go for whatever does the most damage and try to shut down priority targets as quickly as possible.
Now, we have the option of building on that in a number of different ways to create a more strategic 1-char tb combat experience. Giving the player more resources to manage within one character, aspects of a human(oid) body that drain with different combat actions, such as a bar for each character stat, leaving some abilities unavailable as the bars become depleted in their entirety. Of course, you would also have attacks that focus on draining different stats, which might present the player with a difficult choice of resource conservation v.s pacifying the threat of the opponent. There might be something to such an approach, but I'm fairly skeptical. To me, there seems to be a risk of turning combat encounters into number-crunching segments, where your mission mainly revolves around comparing character's stats, but I guess it just goes to show that character systems alone aren't enough to create a good combat system.
One option, though not one I'd personally be too eager about suggesting, is a more 'puzzle-game' like approach. Or at least, that's what I'd call it, though it's actually a fairly good reflection of the direction taken by many strategy games. Suppose we give the player a ton of abilities that he can use during a turn, abilities that basically act as counters to one-another with varying degrees of efficiency, and then pit the player against enemies with the same kind of abilities or variations on the same theme. Essentially it breaks the combat down to selecting the option that best corresponds to the obstacle presented by your opponent, which really is an ever-present aspect of the overall challenge, but as the main focus of combat strategy amounts to little more than fitting the right shape into the right slot. In a rt-environment the actual challenge would come from accurately interpreting your enemy's action and having to perform your counter-action in a timely manner and under pressure, but in tb the challenge might instead stem from an increased amount of more appropriate shapes to choose from, actions with consequences that carry over for more than one turn or even stack and maintaining the right priorities, in particular when fighting multiple units at once.
The reason I don't like this approach, although aspects of the idea itself seem inescapable when it comes to combat, is that the most meaningful iterations of this system tend to oversimplify the simulation. With roshambo-style hard counters you're narrowing down the list of options to only a few viable alternatives, making it a mundane task for players to select the right counter once they know the obstacle, albeit one absolutely vital to success. However, if you give the player a bigger number of equally viable options to counter an enemy action, in order to address this problem, then the choice of picking just the right counter becomes far less important. In part, I think, the saving grace of a design based on these principles would have to come from long-term consequences for the choice of 1 viable move over, say, 10 equally viable ones -- i.e stressing the player's ability to predict events several turns in advance.
With this in mind, the second option could be removing some of the abstraction in regards to what constitutes an action and redefining what a turn is meant to represent. A combat encounter could potentially be structured in such a way that several turns pass in preparation for an attack or a defensive measure, by giving actions perquisites which must be payed in advance in order for the action to be performed, kind of like channeling. In hand to hand combat you might, for instance, detect or predict that your opponent is charging up to close with your character and stab at his mid-section. If you managed to catch the signs early, your options to respond in an appropriate manner may be greater. A last-second response might involve raising your shield to block or deflecting his strike with your sword, while an early counter could involve anything from a well-prepared dodge and counter-attack to mid-strike shield bash knocking him off balance. So, while we still have numerous counter-actions involved, the weight here rests on timing and forethought, sort of how a spearman unit is a definite horseman counter in Civ, but unless you've built one in advance to being attacked you can kiss your polis goodbye.
I really like the idea of this sort of set-up, save for obvious practical considerations. For one, I'm rather worried that a sufficiently complex implementation of a system that strives for this kind of 1v1 combat would make combat encounters incredibly slow affairs. I mean, naturally one would have to cut down on hp-bloat to make this type of combat feasible, as unlike the average abstracted engagement in RPG's you'd actually be privy to the entire process behind the attack, meaning that both your opponent's and your character's options for actively avoiding damage increases dramatically. There's also a notable disjointedness in the time-frame within such a turn-based system, as the actions end up being segmented rather than in sync. What I'm trying to say is that having accurately deduced your opponent's next move, your move inherently consists of a delayed action, designated for a time-frame
outside of your turn. It still works, sort of, as a turn-based system, but I'm getting the feeling that we aren't doing ourselves or tb combat any favors.
So, in conclusion, I'm actually more in favor of a phase-based system for tactical single-character rpg's. If abilities are presented as general actions rather than effects with abstract processes behind them, a single rotation of engagement and disengagement can involve a sufficient number of immediately important tactical decisions and options, while yet maintaining a pace that doesn't slow the game down too dramatically. With reaction times being modified by stats, you can have different lengths of phases for different types of characters as a phase-based simulation of action-points, which to me sounds like a pretty big deal by comparison, as characters going out of phase with one-another in itself creates a tactical challenge and forces disengagements or alternative strats. I really do think there's a lot of untapped potential here.