Is there any other benefit to running a full node beyond increasing the diversity/stability of the network?
Im not sure but having more connections would mean that blocks are loaded faster if you have to download blocks for some days. With standard client it can be hard to wait to download the blocks of last days.
Its hard to wait until to get confirmations but even harder when you cant use bitcoins because you miss the last blocks. With more connections this should be faster.
That is false, downloading of blocks are depended on I/O speeds, CPU, and network, this will not make blocks download faster.
The benefits are that your helping the network and protecting it.
