"Improviser" or "improvisor"?

The advice you got on the web is worthless. There is no rule. Use whichever you are happier with - probably the more common, unless you want to be different.

It took me a long time before I got it into my head that when W.S.Gilbert wrote The Sorcerer in 1877, he spelt it that way, and not "The Sorceror", which I believed was "correct".

Well, then English must feel more natural to you than Latin. The usual English agentive suffix spelling is -er, now pronounced /-ər/.

Improvise and improvisor, on the other hand, come originally from Latin im + prō + vīsus '(something) unforeseen' [English un + for(e) + seen -- the prefixes are blatantly cognate], and imprōvīsor is simply a regular Latin agentive form. With an -or. Which would have been pronounced by ancient Latin speakers, along with every other letter in the word; Latin spelling represents actual pronunciation (circa 0 CE); in this case it'd be pronounced [impro:'wi:sor].

Doesn't sound or look wright to me either.

Oh, and as for advice on which one you should commit to -- do what you please; that's what everybody else does. After all, it's your language, and your spelling.