I had my carb completley rebuilt prio to putting my engine back together. The first time I fired it up it ran great. Unfortunatley I had to remove the intake with the carb attached for another reason. Anyway, when I put it back on and fired up the motor, the carb had gas shooting out of the accelerator pump. A friend - who knows a whole lot more about carbs and engines than I do - took it all a part and put it back together and it ran fine.

Well today - about a 100 miles later - I was driving the car and I accelerated hard and the engine died. I pulled over and the carb was doing the same thing - gas coming out of the accelerator pump. So I'm stuck on the side of the road trying to get the carb to stop doing this. I tapped on the front to see if the floats were stuck and nothing...more gas on the intake. I then removed the screws that hold the top of the carb on and realized that I was going to get into trouble because I really couldn't take this apart on the side of the road especially when I'm not really sure how to do it properly. Anyway, when I put it back together it worked.

What could it be??

needle and seat (fuel inlet inside carb) sticking open. is a good starting guess.
Float is possibly sticking or dragging on carb bowl

Get a high flow needle and seat. You are draining the bowl so much it is allowing the float to fall to the bottom and cocking the needle in the seat.

Also, I believe you can limit the amount of "drop" on the float. This wouldn't help if it is starving for fuel, but it would prevent the needle from getting jambed.

how much of this issue could be due to particles in the fule/tank?

If you have a good inline filter I would say that isnt it. The filter that goes in the carb inlet is good enough to not let particles in too.

I have the ceramic filter in the carb. I thought I'd put a paper one on the line right before the fuel pump to see what happens. Does this make sense?

yes you can never have to many filters.

Is there an adjustment for the accelerator pump? I am used to holleys and you can have them set up to tight and damage the accelerator pump when accessive acceleration is done. On a holley you set the lash at zero at idle, then at wide open throttle you need to make sure you have efficient lash on the upper end to keep from damaging the accelerator pump. At least this is what I read on one of the holley tech articles.