the case of the dying bike

[4twizzle]

So I've got this bike and it's doing this thing, and if y'all could help me diagnose it that would be just great...  Thanks in advance for any help.

Facts:

97 gs500 fixer-upper, recently revalved, reshimmed, cleaned up, etc, and back in running condition
recently rejetted (just jets, no exhaust, etc, used the wiki guidelines, works great) and tuned
carbs have been torn down, cleaned, and examined about 3 times, including when they were rejetted which was the most recent time, and that was last month
can ride it around for a while just fine, works great

Symptoms:

If I'm cruising along at a set speed, I can feel it pulling, and then barely hold speed, then pulling, then barely hold speed.  it goes from being able to hold a consistent speed to having a jerky power output, and then starts slowing down.  It rapidly goes downhill from there until it just sputters out and dies.

Then, a while later, it starts up again just fine and goes for quite a while (let's call it 15-20 minutes) and then does the same thing.  Today I ran it for 20 minutes around the block a bunch, no problem, then stopped it to have a conversation and 45 minutes later I got back on to go home and, while it started up and pulled away, it only lasted about a minute before exhibiting the problem again.  This time I was able to get it turned back on, but the power was sputtery all the way home.

Other symptoms:

If I give it throttle very, very, very slowly, it revs up and up.  Usually.
If I give it the throttle quickly, or even just moderately quickly, it just dies.

Givens:

gas tank is not empty
gas tank was recently given fresh gas for the first time in... probably a year
current miles on the tank: 65
fuel petcock is "ON"
I just drained the float bowls and there was a very fine black sand-like substance that came out with the gas.
there's no fuel filter in the fuel line (yet)

I'm thinking:

cylinder compression issue (but I would expect this to be a more consistent problem).  I raise this because I've reshimmed it twice since getting a new valve assembly for it - once on install, and once after they'd been run for a while to get them seated.  It could very well be that they need to be reshimmed again at this point, but this seems like it wouldn't present these specific symptoms.

something in the gas clogging a jet.  this seems like the obvious thing to me, but this raises the question of whether the bike should be able to run on one cylinder.  If so, you'd think the bike wouldn't die like it does, and if a jet was truly clogged up, there wouldn't be intermittent power at the same throttle setting, the cylinder would just go dark.

maybe something wrong with the vacuum and the fuel petcock.  On the other hand, I suspect I'm using more fuel than exists in the float bowls and fuel lines, so I would expect this issue to appear sooner after starting the bike, like after just a few minutes.

some other funkadelic issue with the carbs, choke, gas, etc.

[birdhandler]

it could be a petcock problem see how you get on with the tap on prime you may have a blocked or kinked vacuum line from the carb to the petcock
the other tng it could be is a bocked vent in the gas tank
Hope this helps
Cheers

[reload]

sounds exactly like the problems i'm having. bike runs fine at low speed but cuts out like that any time i push it past ~35mph. pull over let fuel trickle down or put it on prime and crawl home.

i took apart the petcock and found the gasket to be disintegrating, also some black goop  .

i have a '94. '09 petcock is on the way. ill let ya know how it works out.