Curmudgeon

The tank vent is on fuel cap.

I know this is a long time ago, but I will answer anyway.  Sounds like a float level problem to me.  

The foam filter falling apart is normal at 20+years.  They come oiled if you get the Suzuki part.   I would add to the other suggestions that you check for blockage in the tank vent/vent line.  

Is the 15 minutes at idle or normal driving?

The only way I could do it on my 2000 Quadmaster was to pull the center and side plastics and the tank.  Total PIA.  If you do this I suggest replacing the tank valve as well.  Mine went bad.  Also clean the tank of any sludge or sediment.

Not an expert on this 4x4 but have owned MC and 4x4 for many years, and do my own mechanicing.  

Search for Quadmaster manual or maybe shop manual and you can download the shop manual on this site for free (if you've been here long enough.)  This is the only place I could find it on the internet.  Not even suzuki lists it. The Quadmaster was only made for two years, 22 years ago.  it is a great farm vehicle, even if the straight rear axle chews up the dirt/grass when you turn.