The symptoms are pointing in too many directions. The heat/E10 could be evaping the fuel out of the bowl. I'd fill the bowl/pump several shots & see if it will stay runnning. if it does then a thick base gasket may help & it may just have to be tolerated if it sits for that long (heat riser not shut closed I'm assuming). If it dont stay running I would plumb a can of gas to the pump inlet which would eliminate the rear hard line/2 short neoprene hoses/tank/sock. All that is left is the pump/pushrod (it should be ~3.250" iirc)