I don't want to add another detail to look at, but I feel like it is important. I believe MAT correction is a valid parameter to change. I don't think ASE can fix it due to the short amount of time it is present for. When you shut the engine off, go into the gas station and come back for the hot start, the intake has tremendous heat soak. MAT is the parameter that compensates for intake temps. If it heat soaks to something above normal operating temp then it tries to add less fuel because your "hotter" air is less dense. This was something I experienced and promptly solved it with a couple percent changes. Also, not sure about this but my timing at idle is about 18 degrees BTDC. I've seen this in other cars (not just miatas too) and frankly have never seen 14 degrees. But if it runs fine cold then I would probably eliminate that.

For anyone else with the hot start issue, this is what fixed mine:
- I raised ASE taper to 565 cycles at 190 degrees, 520 at 175, and 480 at 160
- I lowered my idle AFR target from 14.7 to 14.2
- I retarded my timing at idle from 18btdc to 14btdc
- I matched my other closed loop idle settings to the ones.on the basemap from trubokitty.com

Raising ASE taper seemed to make the most difference. It gives my wideband time to go from HTR to actually reading the AFRs.

My only small idle issue now is that after I hit the throttle it hangs at 1300ish rpm for a few seconds before dropping down to 900.

Thanks again for everyone's help and advice.

Melvin. There is no need to screw up your MAT correction everywhere just to fix a bad air temp reading at hot re-start. There is a selection to turn MAT correction off while ASE is engaged.

Also, what are you thinking is a "short amount of time" that ASE is present. The limit in TS is 2500. That is 250 seconds, if set to 0.1 seconds, rather than cycles. Now it is linearly reducing with time, so at 125 seconds, or 2+ minutes, it would be at 1/2 the original setting. That is more time than should ever be needed for EGO to take over.
DNM

I see your point now actually. I had wrote about something I had misunderstood, my mistake. Perhaps I should go back and set mine up like that, perfect time too I guess. Thanks for helping me see that.