Cost-effective replacement for cellular iPad AAC battery?

My son has been using an iPad as an AAC (Augmented and Assisted Communication) device for three years now. To purchase a device through our health insurance would be an estimated $1200-$2000, as our insurance doesn't really provide much coverage for the device.

This device has been a life-changing capability for my son. His current device is a 7th gen iPad that I originally used for work, but his needs were greater. We were able to purchase the iPad app that facilitates the communications for only a couple hundred dollars.

Now we find ourselves at a point where we are needing to replace the iPad (we will be able to transfer the app to the new device) because the battery life isn't keeping up with his daily usage. This is by no means a knock against Apple or the Device, they are amazing. We use a WiFi + Cellular version as he has elopement issues, and I keep a sim active in it, but he takes his device everywhere, and it provides us a way to track him if he escapes the house.

I'm trying to find the best way to replace the device without breaking the bank. As with everyone, money is tight and we cannot afford to go through our healthcare provider, so we're looking to use an off-the-shelf iPad again. What is the most cost effective way to purchase a new cellular iPad? At this point I'm afraid I'm going to have to buy something refurbished on Amazon as the new device prices, even for educational, are just not really affordable for us right now.

Any tips or assistance is appreciated.