This may be a long shot guess. I've heard that the fuel helps to keep the pump cool. If the pump was getting warm, maybe it contributed to poorer performance. With nice cool fuel from underground storage, the pump cooled down and performance improved some.

 

Fuel filter and vac line are good suggestions. Don't overlook them. Cheaper and easier to start with, though I suspect the pump is in need of replacement anyway. I always start with the cheaper and easier stuff and work my way up the ladder of difficulty/expense.

 

The PSI the fuel pump is putting out seems very low to me. It should be around 20-30PSI, but I don't think a fuel pump would be triggering the P0340 fault. The wire leading down to the CPS is known to age, crack, and short out causing all sorts of issues from not starting, not revving past say 2,500-3,000RPM, or like you it has a mind of it's own when starting. I recently saved/repaired two D1's both which would not run a 98 and a 99. Previous owners had given up on them and put em out to pasture. My friend bought em, and with a little trouble shooting it was the wire going to the CPS on the 99 D1, and on the 98 D1 it was simply not plugged in all the way!

Since you have a 98 with AEL it is certainly cheaper to just replace the fuel pump itself, and the sock attached to it. The entire assembly for a D1 equipped with AEL is not cheap. It's not a hard job and you can find fuel pumps online for as little as 15-30.00 with a new hose, clamps, connector, fuel pump, and sock. That should get your PSI back up into the normal range. If you still have P0340 check the wiring on both the Crank and Cam sensors for broken insulation. If either one of those sensors are acting up P0340 will get triggered.

 

UPDATE:

Thank you for sharing that video, exactly what I needed.
I swapped the fuel pump out last night and took it for a quick test drive...so much more power, especially when climbing a hill or kicking it down on the interstate. I suppose my old pump must have been barely working.
I drove it to work today and will toodle around a bit before going home, hoping to find out if this fixes my hot start problem. Fingers crossed, I'll report back. Thanks everyone.