I will give you the answer i always give:
You can not do a real stabilization at home without some fairly elaborate equipment and supplies.You will need vacuum chambers,pressure vessels, mono-acrylic resins, and some other chemicals.The equipment is not cheap, and the proper chemicals are very expensive.
Using minwax, or other similar products will make the wood better that it was, but is not the same as sending it off to be stabilized.
The bad news is that your wood is already cut to final size. A piece of wood needs some room for trimming after stabilization, usually. Thin pieces are prone to warping.
You might try using a very thin CA, something around a 20, in a home built vacuum chamber to stabilize that wood. On the "For Sale" forum there is some for $50 a one pound bottle.
If it is truly super dry, you could send it to Mike at WSSI and see if it will hold up to stabilization. He would advise you if it is a reasonable risk of warping.
Stacy