The only time you need garbage collection is when you're allocating new memory. This is of course abstracted away into the 'cons procedure you end up calling at each (cons a d) - basically 'cons triggers gc if necessary. You may then very well just use the someone-Boehm garbage collector for C, which will (I think!) helpfully look at registers and stack for you.
The someone-Boehm GC (reportedly) works well with C - I'm reasonably sure that it will work well with assembly.
Anyway, maybe the right way to do so is by destructuring a Scheme implementation ? Starting from a given implementation, you write your compiler from scratch, but use the facilities of the chosen implementation for the reader and the GC. Then, once it's working, you gradually remove the scaffolding by implementing these things by hand...
Well, if you're going to end up implementing something like my unrolled-lists ideas, then everything can very well be a cons cell underneath. Including bignums and strings.