First off, document everything you take apart with your camera phone. Second, yes, you can cut the thread holding the padding together at one end to slide out the stay and use it as a template for a new one. 1/8" HDPE is what I would use. I bet the original stuff is 1/16". If you get your lace from usaportsdirect, you can buy a palm lace that is already split. I think all the lace on your BM-76 is 3/16". You could use 1/4" for the finger tips and web spiral, but for the web, as you will need 4 separate pieces, I'd stick to 3/16". And you could use 3/16" for the entire thing. These were always made with thick heel pads, but you can certainly trim it down... Get a good pair of scissors though.
Yours has an older lacing pattern in the web area where the single post runs on the palm side of the web. Didn't take long before they move it to the back of the cross bar. When you relace, You could do it either way. I have one of each, and the one like yours is laced a little differently as well.
At this age, I am sure a little Lexol would be a good idea. After than (and before the relacing begins, a coat of beeswax would be nice too.
Good luck!