Assuming you have multiple (30+) computers, what options are there available to do a distributed solo-mine? Can I have them all checking into one bitcoin application over the network, or do I need to create/join a pool?
You can run as few or as many Bitcoin clients as you want. You can have them all pull from the same client, or you can have each miner pull from its own client. Just remember, the mined coins will go to the wallet of the client the miner pulled the work unit from.
There is no advantage to "pooling" solo miners. Simply install the client and a miner on each machine. Point the miner at the local client and start mining.
While you can have all the machines pointed to a single client (just give the miner the machine-name or LAN IP address of machine w/ bitcoind/wallet) doing so introduces a single point of failure. If the machine with the wallet goes down you lose the entire network until you fix it. If each machine is using a local bitcoind/wallet and it goes down you only lose 1/30th of the network.
If you feel you must have centralized control I would strongly recommend setting up a private pool and pointing all your rigs towards that. While you still have a single point of failure the server can be simplified to only run the client and pool daemon with no other applications. That combined with no OpenCL/GPU driver complexity and no massive heat/power draw should result in a more stable single point of failure. If your rigs are no climate controlled (warehouse). THe pool server could be put in a clean climate controlled enviroment which should improve uptime. While I strongly recommend fully decentralizing your rigs I would consider this option rather than pointing multiple rigs to same wallet on one rig. Of course it makes more sense the more rigs you have.