Since I am a constant tinkerer and can't ever leave anything alone, I'm still working on this little project and trying to improve it as much as I can. I really like this thing but it had one huge flaw.... it was heavy AF. So here's the summary of what I did to the cooler stereo to make it lose weight. Basically I knew there were several things I knew I could change to make it lighter, but I wanted to know how much lighter each change was, and what my total weight savings was so I also took a bunch of notes on individual components weight as I went.
First I changed the battery. When I first built the stereo I wasn't sure how much power this contraption would pull, so I went way overkill on the size of the battery. After getting an ample amount of R&D time with it, I knew I had way too much reserve capacity in the battery, and this massive battery was the biggest weight killer. So I definitely wanted to change it out. For reference, I played this thing for three weekends in a row (probably 12-15 hours of actual run time) without charging, and it only went from 13.0v to 12.1v the whole time. Considering audio equipment is made to play down to 10.5v, this let me know I had way more reserve capacity than I would ever need.
Picture comparison of old battery with new battery:

Next I changed out the subwoofer amp to an amp of the same wattage, but like 12 years newer so it was much smaller and lighter.
Picture comparison of old amp with new amp:

Changing that old big amp to a smaller and lighter one allowed me to mount both amps directly on the wall inside the cooler, and ditch the wooden shelf I had made out of plywood and 2x4s. This was a direct 100% weight savings since it wasn't being replaced with anything.
Here's a pic of how the inside is setup now with smaller battery and amps mounted on the walls:

(Yes I am aware the wiring is a spaghetti bowl of terribleness. Eventually I wlill go back and clean it up better, just don't have the time right now)
Lastly, I changed out the huge heavy duty ratchet straps I had holding the lid down to some much smaller pull style straps. Not only are they lighter, but they are red and black so they match much better. They are also quicker and easier to take off if I need to open the lid for anything.
Pics with new straps:


So for the TL;DR crowd, here's the data on each component and how much weight I saved total. Overall I'm happy with the changes made.

Conclusions: I can already tell the difference in ease of portability is going to be huge. I could lift it into the bed of my truck before, but it wasn't fun by myself. Because of how big and awkward shaped it is, the weight was a killer. Now picking it up is no big deal. Also, when I took it on the river, it was kind of a PITA because of how heavy it was. I had to have somebody help me walk it down the stairs and help me set it into a tube. Then I had to have them help me get it back out at the end. Now that it's much lighter, I feel like I could do all by myself. I'm going back to the river in two weekends from now, so I'm looking forward to seeing how the experience is different now that it's much lighter. Also just wheeling it around in general is much easier.
Obviously the biggest sacrifice here is going to be less run time, but I'm pretty confident that even with the significantly smaller battery I should be able to get a solid 7-8 hours out of it. If I'm going on a multi day trip I'll need to charge it at night, but it should be able to go all day each day. I'm ok with that. I'll be doing some R&D with it these next two weekends so I'll have a better feel for it after that.
As always, questions, comments, and (constructive) criticisms are welcome.