I finally got a chance to build and put up an antenna. I followed on from the the ideas that WP4AOH had for building the center insulator, but added a 1:1 current balun as laid out in the W1FB QRP Notebook. That calls for 12 bifilar turns of #26 wire on a FT50-43 for up to 25 watts. I used #22 wire, as that is all I could find in my junk box.
Here is a closeup of the center insulator
It isn't very high - probably only 15 or so feet - but that is all I could manage right now with the arrangement of trees in my tiny back yard. It is cut for 40M, and is sort of a bent inverted V. It is about 100 degrees in the horizontal and slopes down to about 6 feet at the ends. It is fed with 100 feet of RG-58. No idea how well this arrangement will work, but will hopefully be better than the unmatched random wire I was testing the receiver with before. I cut the legs too long and will shorten them once I have a method to measure it.
Also, many thanks to my wife and 5 year old for helping me measure, build, and raise the antenna. I really lucked out in the family department :)