I’m not a preconditioning expert at all, but had to delve into this a little two weeks ago. Might it be that the coupling relations across domain boundaries are giving AMG trouble? I assume those are the off-diagonal bands. That reminds me of this work: https://www.youtube.com/watch?v=3TZ0D7Dp8js
So, you’d have to move those dofs to a speparate block, and use some sort of (Schur-based) block preconditioning, only applying AMG to the domain interior dofs. Maybe you can get that to work relatively easily with PETSc’s index-sets and fieldsplit (see https://fenicsproject.discourse.group/t/precondition-appears-not-to-happen/).