Tailoring Question

My tailor has instructed me that such a thing is generally not worth the time and cost involved, that basically if a coat doesnt fit me in the shoulders, I should have bought a different coat! But then again I usually buy inexpensive suits off the rack, and he knows my budget is small.

The tailor that's shortened the sleeves, what do they say about the fit?

Generally for sleeve shortening (granted that you don't shrink), wear your best shirt that fits well just on the wrist. Nothing too short or too long. Tell the tailor how much cuff you want to show. If they screw up, take it back and re-do if they value their reputation. Usually with the tight pits, it's with jackets having a tight chest and low armhole. You can let out the chest. But it's generally not worth the time and effort when the chest area is much closer to the armhole. The same goes for taking in the shoulders. Pictures might help, might not look as bad. But from the problems you're having currently, seems like you just have a bad suit. Might want to just invest in a better one.