pity you've sanded the old paint down, new colour would definitely stick to the old one if the original paint is in good condition. arguably better than it does with a 'nude' frame and a primer. less work, same result.
I've done few frames myself, mostly in at least good condition regarding paint. I've used sprays from a nearby shop, mostly some car stuff. BTW it's not about the paint itself as it is the spray can and that thingamajig that.. sprays it. of course - scratches or falls, they leave a bigger scar than normally but there you go - apply some of the paint you have left, and you're as good as new.
as for the process itself - hang it on a rope by the head tube in a warm garage. no outdors - the wind can spoil applying paint. I'd suggest applying around 3 layers, wet on wet. don't wait a day, don't sand it down in between (you'll just make the surface rough), just spray (you want the layers thin), wait around 2 hours and go again. if you do wait till the it dries completely, the next layer won't stick as good.
same thing with wheels, stems, posts - as they're less exposed to harm, it's even easier to customize them with even a five buck can. some deep alu wheelset I painted more than a decade ago (no primers, clear coats, just paint) still looks good