I'm trying to provide a way to use theorems/lemmas/definitions.

The main way I see about going about this is via the custom block declaration:

To enable this feature I'm running into a roadblock of not being able to:

1. supply non-body content like a header (e.g. theorem name)
2. autoincrement/number

For 1. it seems as if caption = "Fermat's Last Theorem" could be passed through to the block more options would be possible.

For 2., I'm pretty sure this isn't possible due to the restriction on the \ref tag.