The title is a bit wrong. It is a top down RPG not side scrolling.

I took another crack at it using a similar concept. This time I separated the pulse extender and the clock. This way it is very reliable and the clock speed and the speed between pistons extending can be easily controlled with the repeaters.

Basically I have the same pulse extender which switches on a clock. Then each pulse from the clock is connected to the pistons with a repeater going into one piston to make it extend after the first one.

By the way, the dropper and stuff coming out of it previously was just stuff I saw in your pic and tried to replicate it to see what space I was dealing with, it did nothing. I removed all the extra stuff in the new pics.

Here are some pics:

I am by no means good at redstone, so I do not know if my solution is compact or efficient (or any good at all!).

My approach is to make the pistons fire alternatively constantly until the string is not triggered for a few seconds then it stops firing the pistons. This way there is always a constant piston firing rate and after the last item has fallen through the string the pistons still fire a couple of times just in case some items fell on top of a slime block then this will clear the items.

In the images you can see I made a pulse extender coming off the observer that is looking at the string. Then there are observers looking at the dust that is part of the pulse extender and every time the pulse degrades the observers trigger. Then after those observers are repeaters to slightly extend the pulse so that the pistons fire slow enough not to leave their slime blocks behind.

Note that the repeater after the left observer is 3 ticks and the repeater after the right observer is 4 ticks.