> So, after this rather lengthy introduction to the dilemma, here it is: When do you say "try to", and when do you say "try and"? Are there any absolute rules, or can you use whichever of them you want at any time?

Both are correct, but "try to" is generally considered better. Use of "and" in place of "to" in this context is called a "hendiadys," which refers to the use of a conjunction ("and") in place of what would normally be the subordination of one word to another ("to").