How do I stop losing so much time on corner exit?

What your run group guy told you is real, and it's the single most common thing separating mid-pack drivers from the fast ones. It's called slow in, fast out. The lap time is made on corner exit, where you can get to full throttle earliest. If you carry five extra mph at entry, you have to squeeze the throttle later and more gently because the car is still loaded up and turning. Braking a bit deeper but slowing to a genuinely slower minimum speed lets you open the steering sooner and get back on power way earlier. Feels slower in the moment, but your exit speed onto the next straight is what actually pays you back. Two seconds a lap on a stock Miata is almost always sitting in exactly this place, not in braking later. Don't go braking later yet. Do the opposite for a few sessions. Pick one corner, brake to a speed that feels almost embarrassingly slow at the apex, and focus only on how early you can get to full throttle. Watch your lap timer sector splits on the straight after that corner. If the straight time drops, you've found your answer, and you can start creeping the entry speed back up untill it stops paying.

On the rear stepping out in the long right hander, that's usually you getting on the throttle while the front is still loaded and the steering is cranked over. The car is asking the rear tires to do two jobs at once, putting power down and helping turn, and they give up on one of them. It's not cold tires or a line problem if it happens right as you apply throttle. Fix it the same way as above. Slow the entry, unwind the wheel first, then feed in the gas. If the rear still moves around with the wheel mostly straight, then look at tire pressures or shock settings.

And if you want proof, run a session where you ride with one of the quick guys or have them ride with you. You'll feel how little steering they're using past the apex and how early they're flat out compared to you.

This clicked for me a few years back when I started logging apex minimum speed alongside my lap timer. On my old NA I found that dropping 3 mph at the apex of the hairpin got me 7 mph more by the end of the back straight, every single time. The wierd part is how boring it feels inside the car. You think you're dawdling, but the clock says otherwise. One thing I'd add on the stepping out: try going to full throttle in two distinct steps instead of one smooth roll. Hit maybe half throttle, let the car settle for half a second, then go the rest. Once that's consistent you can blend it back into one motion and the rear stays planted.

Same thing happened to me when I forced myself to try a slower entry for a full weekend. First few laps I felt like a rolling roadblock, but my exit speeds on the data app crept up lap after lap and my best time dropped by over a second without touching the brakes any later. The mental trick that helped was picking a landmark past my old braking point so I actually braked earlier instead of just lifting. On the rear stepping out, mine did that too until I realized I was still unwinding the wheel while flooring it. Waiting until the car is nearly straight before adding power made it go away completley.

Update: tried the slow in fast out thing for a full session and yeah, it feels painfully slow inside the car but my exit speeds are way up and I dropped over a second. Still fighting the rear getting loose on throttle in that long right hander though. Is that a sign I'm adding throttle too fast, or should I just be more patient with the steering unwinding first?