I've not done it nor heard of anyone who has, but it seems to me the base problem is lack of space for insulation. You aren't going to get much gain in R-factor using a different material if the available wall space is only 1.0" (which I think is likely). Another limitation is conduction through structural members (no insulation) and single pane windows. The roof probably needs to be addressed as well.
This article discusses insulation for a tiny house where the construction limitations are probably similar. It describes some insulation types that might exceed the typical R3 per inch. You might also make some gains simply by better workmanship, i.e. fitting the insulation better so there are fewer gaps.
https://tinyhousebuild.com/insulation-options-for-tiny-houses/