Look at post #66 here> http://motorbicycling.com/showthread.php?t=13591&page=7
and you'll see your method used to strenghten a frame on a trike build I did several years ago. The trick here was that I had a certain width to work with and had to fill it without disturbing the two ends or the separation between them.
After the stubs were cut to size as well as the filler piece I rosetta welded the stubs in place though two holes drilled in the underside of the frame tubes so the welds would be hidden. I finished it off with a TIG weld around the points where the pieces met.
Like they say, "great minds think alike". Thanks for sharing your ideas.