Overnight, I thought it may help if I cut the rivet somewhat shorter. I tried a few differen lengths. The best result was cut down from .187 down to ~.152 long.

I peeled apart my test part to see if these soft rivets were going to be sufficient. It was pretty tough to peel off this piece of aluminum, so I'm confident use of soft rivets are just fine in this application.

My rivet cutter couldn't cut as short as .152 long, so I hacked up a custom rivet cutter from a couple pieces of steel strip.

There's a bit of variation, but the rivets ended up being .150 to .154 long.

I spent several hours fitting and drilling all the metal strips around the top edge of the arm rest compartment. Here's the lid fitted to the compartment.

The lid was getting sprung up a little bit.

Turns out the hinge pins were hitting the top edge of the inner strip.

I filed a bit of clearance.

Here's a view of the inside. The bottom, angled edge of the inner strip has some gaps...needs to be angled more.

I took it apart, seamed the edge a bit more, and reassembled. Fits better now. There are still a couple gaps, but with a bit of additional tweaking, it should fit nicely.