The first problem I see is that a good lawn mower that will take care of your 'good' lawn is NOT suitable for what you describe as "weedy" areas. Also, you won't be happy dragging the belly mower out from under it any time you want to do garden work.
Just my two cent. Look forward to seeing what decisions you make.
you have a good point about the mower deck. Do you think if it were all the way up, that it would get in the way if pulling a motorized tiller? I could see it smacking into the furrows. :-)
I guess John Deere doesn't have a drive over deck for nothing.