Don't take this the wrong way (as I really like the idea of this pool), but what are the advantages of mining here vs. real solo mining, assuming I already have a full node up and running?

Advantages over regular solo mining:
Mining at solo.ckpool.org avoids the overheads of running a full bitcoin node that requires both great storage and bandwidth for optimal performance.
Solo.ckpool.org is extensively connected to high speed low latency bitcoin nodes for rapid block change notification and propagation.
Unlike regular pools, ckpool never mines transaction-free blocks due to its ultra-scaleable code which has miners on both new blocks and transactions concurrently.