You can use Wugs Nexus Root Toolkit (NRT) to unlock the bootloader (erases device) and install a custom recovery (TWRP highly recommended). NRT can also root the tablet giving you superuser access to apps that can help inherent issues with the nexus 7.
With the custom recovery you can try Omnirom or Clockworkmod 11, both are lighter than the stock rom and based on Android 4.4.4 which was the best release for the grouper (developer name for the first nexus 7) and stay updated with Android security releases.
NRT can also roll back nexus devices to previous versions of Android, you could flash the tablet back to official Android 4.4.4 and never update it to marshmallow if you so desire, only issue is you miss out on the latest Android security patches.
With root you can remove the cap you don't want from the official firmwares by using Titanium backup and you can run Trimmer which is an app that helps the Nexus 7 run better by cleaning up its internal memory which the nexus 7 hardware has trouble with, and why it gets horribly slow over time.
Wugs Nexus Root Toolkit is very, very easy to use. It pulls together what files you need and makes everything a button click process. Even if you accidentally do something wrong and the tablet won't boot, called "soft bricked", Wugs NRT can restore the factory firmware. The Nexus 7 is incredibly robust and the perfect device to start learning how to flash and mess with Android devices, I have bricked my Nexus 7 32 gig grouper dozens of times and NRT always brought it right back.
Right now I am running a mod called multirom, my grouper runs stock 4.4.4 and Cyanogenmod 11. When the tablet boots it asks me which one I want to run, it's a great mod so you can try many different roms made for the grouper but always have your primary one so you can get work done if needed. Multirom is free and flashable through its app or through recovery.
If you are set on buying a new tablet then do so, in the meantime play around with NRT and new roms, don't be surprised if you keep the tablet a while longer when new life is breathed into it.
