In addition, doesn’t answer your question but may help, Vega hasn’t exactly got all that hot a wakeup either much like Balrog doesn’t - Technically, of the two, you should be scoring more knockdowns than he should on a sweep basis and if you do, don’t be afraid to jump in and mixup/abuse his wakeup. Without meter he can’t do (The EX Flipkick thing, Scarlet Terror?) which is one of the few options (which doesn’t even have high success rate against Rogs Jumpins) and jumpins ensure that any attempt for him to walldive is met clean with a Jumping Fierce (Either one is fine though typically I use JFP for the extra range - Also knocks him out of EX Versions if done right) and that should stop some of the walldive/izuna pressure you’re on about if you give him no room to breath.
Vega doesn’t have a lot against Balrog but he’s that type of character where if you give him enough space and time, he can wither you down - It’s all about rushing that low-HP pansy down and ensuring every mistake results in pain and he has little room to breath. Keep a TAP ready for situations but don’t ‘rely’ on it as it’s not a fail-safe against some of his stuff and as above have said, LP Headbutt is your friend against repeated drop attempts.
If they’re abusing crossup drops, focus backdash but bare in mind if he doesn’t cross you up it’s a free crumple. TAP will also work and either throw you to safety or smash his teeth in but again, don’t rely on it - Just read the pattern (if any) and be prepared. You can prevent him reaching the wall at certain distances with a BackJump or Neutral Jump which you can use to knock him out of the sky or punish when you both land so pay attention if they love doing that forward jump move when far enough away from you.
Im not matchup guru or a pro Balrog, just stating what seems to work for me vs the few Vega’s I encounter.