You might need to shim starter, once the engine is warm/hot, thermal expansion pushes the starter away from the flywheel, bet cold engines have it closer, possible it is close enough to almost jam.
I would also check voltage at starter when cranking, sometimes I even just run another fresh battery and cord to starter to see if it is possible you have a weak battery.
Holleys sometimes have issues with powervalves, they leak, they don't work. A stumble that is solved by slowly easing into the throttle sounds like not enough fuel, and actually another possibility for the slow cold start-leaking fuel from the nozzles of the carburetor after shut down. Less likely then the above mentioned starter issues, but still worth mentioning.
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