Or to put it another way, there's nothing in the Taki diner conversation that I recall, that necessarily puts the time of that conversation as immediately after you've woken up in your apartment to the game proper.
There's Silverhand. His dialogues is written for that to be the first interaction with V after the "incident" at night. You would need to remove Silverhand for all the sidequests and then make it so that he is "reactivated" once you trigger the Taki diner...I don't think it can be done
I'm trying to think ... there's the first Johnny interaction at night, just before you wake up into the game proper, that's fine. If you go to pick up your car from the garage when the Delamain cab wrecks it, there's a small interaction there. The next
major interaction is immediately after the Taki diner conversation, still in the diner, when Johnny sits on the table in front of you and he's a bit more friendly and you start to banter a bit (or just tell him to fuck off depending on your rp). That's an important one, and it wouldn't make sense to have that later, you're right - he refers to the topics Taki's just outlined.
I'm thinking that Clockwork Knight's suggestion above is better, of making the delay after the diner convo with Taki and Johnny, so that you have a level-gated delay for the next time Taki calls you back (for the waterfront meetup). The way that the diner convo ends with Taki, it does leave the timing very open.
The Judy/Evelyn and Rogue/Hellman questlines also have natural "don't call us we'll call you" moments - from both Mr. Hands (who's going to arrange the Voodoo boys meetup) and from Rogue (who's going to find out about Hellman). So those return calls could be delayed as well, to roughly around the same hypothetically later, level-gated time as Taki calls you for the waterfront meetup.
Thinking about an appropriate level, you can usually get to around lvl 15-17 just by clearing Watson (doing the Watson chunk of Regina Jones' quests, plus all the little quests and police gigs in Northside and Kabuki) before the Heist, you're probably going to get a couple of levels from the Heist, so let's say you're around 18-20 by the time of the Taki/Johnny diner convo. You probably wouldn't want to delay getting further into the main quests (after return calls from Taki, Mr. Hands and Rogue) much beyond 30, maybe a bit less, say 27.
So yeah, that's two biggish delays that could be introduced. First with Jackie (splitting the car/Vic portions of the noodle bar convo from the Dex portion and having that later (as an audio call that Jackie's found a gig and you've got to meet up with Dex outside Gramsci's Burgers). That gives the player room to breathe to do Watson and Kabuki, up to lvl 15 say (then do the Heist). Then later, another biggish delay while you wait for calls back from Taki, Mr. Hands and Rogue, roundabout lvl 25-30.
