Bike Bogging Down While Riding

[Nate4s]

[Back Story]
Hey Everyone! I've been lurking on these forums for a long time (2 years). I started out on a '99 GZ, upgraded to an '02 SV650 (and sold the GZ), and now I JUST bought another '99 GZ for my "winter" bike and for my girlfriend to learn on. It was an MSF bike and has 4.9k miles on it (VERY hard miles, I assume). It was only $440, and I drove it 70 miles home...and I assumed it was in perfect running condition. It was missing mirrors, signals, had a cracked seat, covered in dust/dirt, had vines intertwined into the spokes, has dents in the tank, and the right handlebar side was smashed up. The downside is that the guy I bought it from had it running when I got there - he claimed that the battery had died and he just bought a new one and had just charged it and started it up to make sure it was working for me (that's a HUGE no-no when buying bikes). I tried to start it the next day, and the idle was all over the place and would die if I didn't "maintain" it with throttle - there was gas in the airbox (as well as a huge handful of sand), and tons of sediment in the gas tank. It's running better, but still giving me issues. Just to give you an idea of what I've done/checked so far, here is everything I've done to the bike:

Reupholstered the seat with marine grade vinyl
Put a new plastic bumper on the back (the old one was shattered and couldn't hold turn signals)
Put on some rear turn signals (it didn't come with any)
Put on new throttle tube
Put on new brake lever
Put on new bar ends
Put a new choke cable on (old one was not salvageable)
Lubed all cables
Put in some plexiglass in the speedometer (old one was shattered)
Replaced the speedometer cable
Replaced speedometer bulbs
Reattached the Kick-stand kill switch (had been disconnected)
Put in New Spark Plug
Drained tank, put new gas in (as well as B12 Carb Cleaner)
Put in 2 cylinder head bolts (had an oil leak near the exhaust header because two bolts were missing, and not stripped....really strange)
Completely disassembled carb and cleaned thoroughly
Installed new air filter (with Hi-flo recommended on this site)
Charged battery (with old car battery charger, set on 12v 2amp)

Follow Up
So, after all of this stuff, I start the bike up (with choke, of course) and the idle ranged from 1000 - 4000 (auditory guess) on it's own, and wouldn't settle on an idle speed. If I turned the choke off, it would die. If I touched the throttle, it would also die. I pulled jets and soaked them in carb cleaner (again), and used pressurized spray and air through the holes, and reassembled. All of the cables and hoses were reattached, and I'm almost certain it's not a battery issue (no dimming of lights, everything electronic seems to be working) or a vacuum issue (runs equally well on PRI and ON). After re-cleaning the jets, the bike seems to idle at a constant acceptable speed (with choke and with choke off) and will accept throttle! I rode off, thinking it was miraculously fixed - not quite. I made it 1/4 of a mile, and the engine started to bog down (and made a "ffffffop ffffffop ffffffop..." vacuumy sound, almost the same suctiony sound the "piston valve/diaphram" inside the carb makes when you slide it up and down) - increasing throttle did nothing, neither did decreasing the throttle. I tried to ride it out, as the bike didn't die completely - it lurched heavily (pulsing) before making a single back-fire like pop and immediately going back to a normal engine level. I rode it about 5 miles, and this process occurred 4 more times (with it actually dying once, although it started back up immediately without any issue). The only other noise I've noticed is a suction sound coming from the gas tank cap.

Possible Fixes
My goal is to attempt to drive it around 50 miles or so tomorrow to get the battery charged back up and to see if the B12 will somehow work some magic and solve my issue (but staying close to town in case it completely dies). If it's still giving me this issue, do you think messing with the pilot mixture screw might help (the brass plug is still in there currently)? Would an issue like this arise from valve clearances? Any other thoughts on things I should try? I apologize for the LONG post, but I wanted to give you every detail I could think of (and I probably missed some things I've also done). Thanks in advance for any help! -Nate :2tup: