I know the best solution would be to dig down on the outside and patch each hole/gap on the outside. I'd prefer to avoid that since there are some large nearby trees near both holes so I'm sure the ground is one big root ball in those areas.

Another solution might be to A) patch the inner gaps with expanding hydraulic cement like normal and B) fill the concrete blocks near each hole by squirting a low-viscosity concrete mix from the sill plate down into the blocks. The idea being that if a rodent did enter through the outside face, it wouldn't be able to navigate up through the blocks because they'd essentially be solid. There's no room to insert a concrete vibrator down into the blocks so the concrete would have to be mixed pretty thin to make sure it flows all the way down...probably cake batter consistency or thinner.

Question: has anybody done something like this? Is there a better solution that doesn't involve digging down along the outside?

A small hole you may be able to fill in stages with polyurethane caulk.
It will stick very well if the edges are cleaned of dust.

Larger holes a small support across the hole to hold a section of cement board.
Some wire through small holes in the cement board and wrapped around the stick across the opening on the outside.

Fill the hole part way with mortar.
Let it harden and cut off the wire flush, then fill the rest of the hole to flush with the face of the block.

Repeat on the other side.