Several people on the ST-Owners forum recommended that I try taking the Swingarm off. This requires a custom tool from Honda and a 17mm Hex Allen key. I didn't want to spend the $80 that Honda wants for the tool and then wait for it to ship, and there are several examples of people taking 1-1/8" sockets and cutting them down to make a tool that will fit. The local pawn shop had just the socket I needed for only a few bucks, so I went to measuring and grinding, grinding and measuring, then grinding some more until I got the socket to fit (mostly). It turns out I should have gotten the 1-1/16" socket... this cheap Chinese socket had very thick walls. I tried to remove the swingarm lock nut and ended up banging my knuckles when the socket slipped... twice.
I decided that I really should have the right tool for the job, especially when I needed to reassemble the bike, so I searched on ebay for the tools and ended up getting both an third party swingarm locknut tool and an axle tool for less than Honda wants for just the swingarm locknut tool.
After I finish with this project, I'm going to donate both of these to Mellow, the Admin of ST-Owners.com. This will let any of the local DFW Honda DIYers borrow them when they need them.
Hopefully I'll have the engine out this weekend.