What is the best way to download a "recent" UTXO set snapshot?
Yes, by default bitcoinj downloads full blocks, from the Genesis. Only if you connect a wallet it uses optimizations like checkpoints and filters.

Just downloading the UTXO set (in a trust free way) isn't possible, because the Bitcoin protocol isn't designed for that. You can get UTXOs from block explorers and Electrum servers, but it will be without crypto proof.