Starting issue, 2000 Chevy Impala w/ 3.4L V6

This car has had a starting issue that has been getting worse over time. When the engine is warm, and/or in hot weather, you turn the key and the engine just cranks. No start. Yet, you just baaarrrely touch the throttle w/ your foot as you touch the key and starts right up as normal. Dealer has looked @ it. Cleaned throttle body and dumped a software upgrade into the computer to increase starting throttle setting by 50 RPM. (650 RPM, I think, from 600.) Issue started long ago by the car stumbling on not enough throttle setting & barely running for the first few seconds, then it remembers, “oh yeah, I need THIS # of revs,” and the car smooths out. Still does that too. No codes. Ideas?