Assuming that the reason for late fruit isn't lack of sunlight, I see no problem with your plan. I use a 8-10-10 in some first year raised beds that have lots of wood tilled into the clay under the assumption that the wood + added nitrogen nets to pretty much a 0.

Sometimes I see clusters of 8-12 buds doing this. I try to pinch it down to 4-6 for anything larger than plum size.

I seriously doubt that it will have any effect since the timing of fruit set is determined by other factors (see the FAQ here on Blossom Drop) but it won't hurt anything as long as you don't overdo it. Excessive phosphorus in the soil and the subsequent run-off contamination is a serious problem in many parts of the country

Dave

Unless you're growing in very sandy soil, the odds of you being low in P or K is not very likely so adding a bunch of P&K-only fertilizer is just going to go to waste, IMO.

That type of fertilizer is sometimes called bloom booster, or something similar. Odds are it's a complete wash. It may create better or slightly bigger blooms, but it also might do nothing if your soil wasn't already deficient in those nutrients - but it almost certainly won't get you earlier fruit. If you want earlier fruit, you need an earlier variety of tomato - or you need to plant out early and protect in low tunnels or the like.

Basically, with ideal conditions (good weather, ample light, etc.) fruit ripens in a set amount of time, it can take longer if things stray from the ideal, but you can't really speed it up.