Would it be easier to add a second sump pit? Anyone done that before? I've used a concrete saw before and they make more dust than just about anything I've ever seen.

Put in a second sump pit about 16' - 18" from the first. You can drill several holes in a circular pattern and then take to it with with a small sledge. You can Fill the gap with concrete or sand mix, depending on how big of a hole you make.
Connect the sump pits together with a solid 4" PVC drain pipe. That should be at a level just above the level that the first sump pump is triggered by its float so that the sump in the second pit only goes on if the first fails.
The pre-formed plastic sumps have knock-out slots for two side connections and you will use the one not already taken by the drain tile. If it is a clay drain tile you have to take to the side with a masonry hole saw if it doesn't have a knock out.
I have this set-up with the Big Dog AC/DC back-up sump for number 2. It automatically acts as an AC back-up sump if the first sump fails and a 12 battery powered DC back-up sump if the power fails. It is nice because this set up gives you back-up without reducing the volume in the first sump by having another pump in there.

My thought is why? Why would you want to build a wall around the sump to stop water getting to it?

What you need to be doing is stopping the water from getting in in the first place. Is the yard graded so rain runs away from the house instead of towards it?

Build the wall, attach a 2” drain Pipe through the wall Running to a floor drain. Let pitch and gravity do the work.