Gacck! I just had Windows Explorer lock up when stopping MA3b1 on this machine when Display Fusion was NOT running, and I also had the Explorer not lock up while Display Fusion WAS running. So now I don't know what the problem might be (or how to diagnose it, since nothing works once the lock-up has occurred).
OK, I've spent a fair amount of time trying different things, and I now believe the problem to somehow be with the multi-monitor setup. The only significant difference between this MCE machine (HTPC2: E6700, P5K-E, ATI HD2600XT) and my other one (HTPC1: E6600, P5B-E, ATI HD3450), other than slight hardware differences, is that this one has two monitors. So, to test that, I disconnected the VGA cable from the 7" LCD and rebooted. All of the startup programs (in the system tray) are exactly the same (I stopped Display Fusion on HTPC2). Now I can start and stop MA3 with no ill effects. In fact, it starts and stops fine even if Display Fusion is running (so I suppose we can exonerate that). I have read here that many others are using MA3 with multiple monitors with no problems (or, at least, not this one), so what can the problem be?