I could machine one up for you, if I had the EXACT necessary dimensions...otherwise, with any kind of improvised tool, you run the risk of doing serious damage (and on an HP-01, even a little scratch is serious).
It already has some scratches on the case back from the previous owner(s) slip ups. There is an original tool for sale on eBay but the price is far more than I would want to pay (item number 191005747456).
I am pondering whether it is worth going down the refurb' route.
I just looked at the listing...I agree; crazy price. I could replicate a much better tool for about $80. I would be best, of course, to actually have the case back here, so I could make a precise dimensional match between the parts. But, if you can get me good numbers (to the nearest thousandth of an inch, or .025mm), I could give you a high degree of confidence it would work correctly.
I have an HP 01 original remover, gift for the book I am writing. Another gift at a conference for HP that I received was an HP 01 case back removal tool:
I have his orrery and Napier bones. The case back is designed, like Bruce's, not to interfere with the piezo glued into the case back. Jim was on the design team for many HP products back in the 70's through 90s.
Now you have a choice!
When you click on the tool you will see my arm at work!
About 18 months ago I bought a HP calc watch back remover from ebay seller szergej2005 who is in Hungary- this is new manufacture steel and will shift any stuck back. Worth emailing him to see if he has any left or could make another run. I seem to remember it was under £30 including postage from Hungary (took four days to arrive). He also used to make light alloy ring removers for P2/Omega LEDs. I have one of these as well and it is very nice. If all else fails I could lend you mine (fat thing so has to go small parcel rate)- I am in London.
I used to use a standard three pin watch caseback tool to remove HP backs prior to obtaining the specialised tool- works well as long as you have one with pins small enough to fit the slots and use a caseholder on the watch so you can press it down firmly when turning.