I am interested in trying to mechanically do this, even with the hope of eventually automating the entire thing so I get sent an email telling me what to do next

Of course! ;-)

Very diy.

Buy a used HP T620 or T520 or T630 thin client on ebay. Make sure you get one that includes the AC power brick/adapter, and 4GB-8GB ram, and an SSD.
like: https://www.ebay.com/itm/156460983475 or https://www.ebay.com/itm/326109395019

Or a new mini-PC with N100/N150 CPU. $100-$150. (Those are so cute I am tempted to buy one just because.)

I bought a couple T620's a while back for $35 each, incl shipping.
It takes a special power pack, but you can use a non-HP one by adding one resistor. It takes a non-standard SSD, which are available from Aliexpress pretty cheap. Add a USB pocket hard drive for more storage -- 16GB is pretty small.

I used to buy hp refurbished desktop(s) before I discovered the thin clients. You don't need much CPU power.

Install Debian Linux. Then write bash scripts to download data, do the screen calculations, and email you the results.

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