"Construct a 20 and/or 40 meter 1/2 wave dipole and feed it
using standard TV
twin-lead as my feedline (found in any hardware/home improvement store)"
Don't know about the stores down there. However, Twin Lead is very hard to find, especially in the populated areas. TV receivers are heavy into coax usage for better of worse.
Think about using mini coax and feed the antenna unbalanced. If you make a fan, dual band dipole, it will eliminate the AT and balun. A purest may want to install a few toroids at the center feed point to eliminate RF on the outer shield, but for QRP operation, I doubt that would be a problem.
Don't wish to discourage you in buying a BL-2. They are a handy item to have but for this particular application it's not necessary, IMHO.