Ok, I've held off posting for quite some time, because I was working with Rigol while they tried to troubleshoot the issue. It's been slow going, but there is some progress.
Rigol has now had my oscilloscope in their hands for 3.5 weeks. After a little more than 2 weeks, they told me they were finally able to repro the lock-up problem (for me, it was happening very frequently). They only saw the problem after connecting the scope to a network, so their theory was that the problem was related to this. However, they were not able to repro the problem a second time. They came up with this theory that the problem was somehow triggered by my network.
After some discussion about the Rigol guys coming up to my house (they are in Oregon) to troubleshoot, they decided instead to send me another unit to test. They said if the problem did not repro with this unit, we could discuss a swap, and if it did repro, we could discuss further troubleshooting.
So today the unit arrives. It's a demo unit that has physical damage, is hardware version 1.0 (mine is/was 2.0), and has the anti-tampering sticker on the bottom broken. So regardless of what happens with the troubleshooting, I am not going to be keeping this one.
So I've plugged it in, and am looking to see if the problem repros.