I've been kegging my beer for 4 years and I've never once used any equations to figure out the time it will take. I'm curious why you can't put your keg under pressure while its chilled in your fridge, but if you can't you can't...I do suggest you chill your beer down as close to 32F in your fridge before you put it on gas. OBviously the colder liquid absorbs more gas, and if you get it chilled down that low before you put it at pressure it'll carb quicker.
That being said, I am able to put it on gas in my keezer. I chill it in the keg for a couple days, then I put it on gas @ 28psi for two days. Then I pull a sample. If its not carbed yet, I leave it on gas longer until it is.
I wouldn't call myself lazy about it, but I'm def not all uptight about it either. IF you overcarb, oh well...take it off gas and bleed it for a day.