iPhone 11 Pro Max with full storage stuck in boot loop: Problem updating/restoring

Hello. My iPhone 11 Pro Max refuses to update/restore.

Context: I decided less than 2 weeks ago to restart my iPhone after noticing a couple of my apps would crash or while searching the web my phone would freeze. From past experience, I suspected it was due to a full storage. I restarted my phone, but it never went past the Apple logo. Every 15 or so minutes, my phone would go black only to boot back up to, and stay on, the Apple logo. Searches online led me to believe my phone was stuck in a boot loop.

Here's what I've tried: 1) restarting my phone 2) completely draining my battery 3) charging my battery overnight for at least 10 hours so that hopefully my phone would automatically start up on the home screen 4) updating/restoring in recovery mode using my MacBook. I had hoped #4 would be the solution, but I ran into another problem.

The Problem: Using the cord that came with my iPhone, I hooked up my phone to my 13" MacBook Pro running macOS Monterey 12.4 (the latest version at the time of writing this post), put my phone in recovery mode, and selected "Update" or "Restore" when the window came up. I've tried possibly 10 times or more, on different days, to update, and even restore, my iPhone 11 Pro Max. In the cases where I finally get to downloading (often, the download states it would take 4 hours), after about 15 minutes or so my phone would reboot to the Apple logo and kick me off from the download.

I've tried a different cord. I've also tried connecting the cords to the different ports on my Mac. I have also tried updating/restoring in DFU mode. My phone has never been jail broken or water damaged. So, I'm stuck with a phone that's stuck in a boot loop.

Ideally, I would rather not restore my iPhone 11 Pro Max; but if that's the only option left I will (and I've tried). Can anyone offer another possible solution, should I send my phone to get fixed, or is my phone a lost cause?

Best,

LS