After a ton of online research, this morning I pulled the trigger on an Icom IC-7200 from Ham Radio Outlet. HRO had an open box unit that I ordered. The discount for this on top of seasonal discounts brought the price down to about $890, the cheapest I found it anywhere.
One of the things that I find especially appealing about the IC-7200 is that it was designed from the outset for use with a computer. It has an USB port on the back, allowing you to control the radio with your PC, including the use of digital modes like PSK-31, without requiring a sound card connection.
I didn't order any other accessories as I've been able to find them cheaper elsewhere online. E.g., I need to get an external antenna tuner, an antenna, a patch cord to run between the radio and the tuner, and an antenna feed line.
Edit: Got a call from HRO that the open box unit I ordered was defective when they tested it. They're going to send me a different one, still at a discount but not as much. Should have it Monday.