way (which is) back (to) home
back (to) home = predicate adverb
I must confess to sharing your discomfort at reckoning 'home' (with the meaning '
to one's place of residence') as an adjective of any kind, rather than as an adverb, and traditional grammarians are likely to need little persuading to accept any analysis, however tortuous, which permits it to retain its normal status.
Others, however, might object that we would never actually say anything like
*My way is (back) home.
and that, since directional adverb 'home' (unlike its locative form in AmE) cannot properly function as a complement, a spurious ellipsis is being cited as the basis of a false analysis!
On balance, therefore - however reluctantly - I would say that, in this particular case (and a tiny handful of structural equivalents such as 'the road home' etc.), we must simply be prepared to carve out an exception to syntactic norms and allow 'home' the status of an adjective.
However, for reasons explained in my previous post, I would still insist that 'back', at least, be reckoned an adverb!