That's a stumper!  Here's a couple guesses.

If your suspension is modified, make sure your tank is still lower in the back than the front or gas will pool in the forward area unused.

Some wiseguy put a balloon in your tank.

Is your float needle sticking closed intermittently?

If that's not it I'd pull the petc0ck and do a clean and inspect.  Is the screen on the tank tube partly plugged?

Best luck, Let us know what you figure out.

I have a new-to-me '96 with a similar problem from time to time.  Actually it tends to be the same place going west and the same place going east.  Since I've been filling up before hitting the freeway, haven't had the going west problem.  I still have the going east problem but not every time.  It's uphill, and last time it was bad.  Usually, pull in the clutch, twist the throttle a couple of times and it goes away.  Even after it flattened out it was still coughing.  Then just as it started it went away.  When I got home, I found the vacum line to the petcock pulled off the carb.  I cut the end off to begin looking for a replacement and today no problems, east or west.

I've had the tank off a dozen times, and every time gas has leaked from the petcock.  So I'm guessing that this doesn't work very well.  And maybe, even with a vacum leak there maybe enough fuel flow to take the flats but not enough to do hills.

I'm real disapointed about the fuel capacity of the bike.  And for the most part I leave the petcock on secondary.  As it is, I don't get 100 miles on primary.  It's only a 50 mile round trip.  I should be able to fill up every other day.  But I have no confidence in it.

I'll replace the vacum line shortly, but I'm also concidering doing the petcock conversion to manual.  I've had it all apart, inspected all the ports.  Blew air thru everything, nothing, clean as a whistle.

I've had the carb apart, and except for a bit of this and that was ok.  The slide was as dark and except for two wear spots very evenly colored, just the right shade for dri-lube.  So I thought it was.  BTW, thanks for all the helpful posts, as now I know I need to clean this varnish off.

Well, thanks to Bobo383 for the petc0ck conversion!  I it happened to me again and I came straight home and tore into it.  I removed the internal screen and added an external fuel filter in anticipation that soon a second tank will be my reserve.  But everything went smoothly.

There was a little junk in the screen and in the bottom of the tank but it obviously wasn't clogging the flow.

Guess I'll have to do the white spacer mod next...