**** Warning: I didn't build one, so I'm not answering the original question... ****
I was unfamiliar with the term "minicell", but Google tells me it is PE foam using cross-linked PE with a small cell size. This site:
https://www.foambymail.com/PR/polyethylene-foam-roll.html claims R-4 per inch. That's what I'd call the baseline - you can get better (R-5 per inch for XPS, R-6.7 per inch for urethane in some cases), but R-4 per inch is probably the best you should design for unless you have an aerospace budget (most materials are worse. Urethane *can* be better, but unless you spray it in it would not meet your needs).
So - sounds like a good plan. Excepting only that as a general rule PE is really hard to get anything to stick. This site:
https://www.thefoamfactory.com/blog/index.php/pick-the-right-glue-for-the-job-how-to-select-adhesives-for-bonding-foam claims 3M Super 77 can be used. But I suspect you'll need to clamp it in place. I'd suggest you plan some prototyping and testing before you commit. Please let us know what you conclude.
Friz installed foam insulation in his Chesapeake Light Craft build, and I suspect it is minicell, so review his build thread.