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?
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.