We decided not to wait for him to try using that method to get out of his crib, so this weekend he moved to a twin bed.
For the most part, he is sleeping fine in his new bed. He did stall a little at nap time today, though. We had left his crib set up in the bedroom (just because we hadn't gotten around to disassembling it, yet). When I went to check on him a few minutes into his "nap" He was sitting in his crib with a pile of puzzles he had grabbed from a shelf. He was happily doing puzzles when I peeked in. I moved him to his bed and reminded him it was time to sleep and he fell asleep with no further shenanigans.
Henry loves that Oliver's new bed matches his.