Stalls if you start it within an hour, but cold starts perfectly

My automatic C4 starts perfectly when i start it cold (in the morning) -- it registers about 14 volts on the battery. But if I stop the car and then try to re-start it within an hour of when it has been running, it'll turn-over, but then just stalls. I noticed the volts are only about 13.5 when this happens.
If i rev the gas and shift quick into drive it'll sometimes get moving enough to start, but usually will just stall out again. I'm actually having to keep my foot on the brake and the gas and rev it and then quickly shift into drive.
That said, if i park it for work and start it 8 hrs later it starts great (again 14 volts), but if i stop at gas station it;ll stall out numerous times (although it'll turn-over without a problem). any help appreciated!

Chris Trautman @ Corvette Assembly Plant 2019

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