The thickness map is essentially a 3D list of the raw thickness values with a LUT so you can visualise them, so getting stats of those values is all you really need, I think.
Keep using BoneJ under 'vanilla' ImageJ for the time being, if it suits your purposes. We are working on BoneJ so that it will integrate seamlessly with up-to-date Fiji, but that's some distance from being user-ready. It is possible to use BoneJ with Fiji, but you have to hold your Fiji back to Java6 (and not let it update to Java8), which is a bit messy. Best for now to continue as you are.
I disagree with you here. Bone tissue comprises cells embedded within matrix, so it cannot be extracellular. Bone has a mineralised extracellular matrix, but is inherently a highly (surprisingly) cellular tissue. It's also of mesodermal origin, unlike epidermis which is ectodermal. Bone-like apatite mineral in arthropod cuticle is very interesting, I'd simply resist calling it 'bone'.