oh poop.
I just wrote a huge response and accidentally hit backspace and deleted the whole thing, so excuse me if this is the abbreviated version.
first, don't say you don't have any time. i've got a 3 year old, full time job and a wife and still find a couple hours to work on projects every night, haha. I wish i was 19 and in college, that was easy!
anyhow,
when you're dealing with something like this you need to make an open issues matrix. that education cost me over 100k and here i'm gonna give it to ya free!
Here, i'm attaching an example.
the first column is symptoms, in order of severity. The second column lists possible root causes for the symptoms (also in order of severity) then the last column lists tests for those root causes, in order of ease.
You go down the list of tests/fixes starting with the easy stuff that will be the most severe if you don't figure it out. As you go down the list you'll be able to pretty quickly figure out what your main issues are, then once you have them fixed you can start identifying secondary issues, and so on. Once you know the results of your tests you can identify the most comprehensive and efficient way to fix it.
Say you identify you have a head gasket leak. You might replace the head gasket, get the engine back in the bike, then realize you have a clogged carb, it would have been easier to identfy and fix both at the same time while the engine was out.
Taking random pot-shots and pushing your bike home will just frustrate you and waste a lot of time and money. Usually there are many things wrong with a bike like this, and it wasn't until the 3rd or 4th thing broke that someone eventually parked it. Add to that the fact that you apparently had some idiot mechanic working on it, and you can start to see where a scientific approach is mandatory.
To this i would also add, the vacuum petcock is (in my opinion) just an additional source of errors and frustration. If you trust yourself being smart enough to turn it off when you're not riding for an extended period, and your floats are set correctly to not leak gas, you can replace it with the 'yamaha raptor' petcock which goes for about $7 on ebay.
Based on what you're saying your mechanic may have jury-rigged the petcock for 'always on' operation which could be causing the gas-in-oil situation. WHICH WILL DESTROY YOUR ENGINE VERY QUICKLY IF IT HASN'T ALREADY!!!
there are some other 'resurrection tips' in my thread here:
https://www.ninjette.org/forums/showthread.php?t=212535