In your picture about with the framed bar. I'm assuming that the frame leaves bee space between the side of the TBH and the frame?
You assume correctly, on the sides and also on the bottom. However, the bees don't seem to care for the frames and this morning, I gave up on them and replaced them with "regular" top bars. I am not giving up on the experiment entirely because the frame bars were the ones closest to the entrance (on the end), and the core is on bars 5,6,7,8 out of ten. The colony is still young and none of bars 5-8 have more maybe 30-40 percent comb. I will save the frames and offer them again later when the colony gets stronger.
One mistake I made is making the initial bars too wide (1.75 in). The bees are burring comb on #8. Another change I am contemplating is moving the entrance to the side where the core is and adding another follower board on the entrance end to keep the core compressed. I will give it a week or two to see how they respond to the fresh ( 1.25 in) bars. I read somewhere on the I-Net about making all the bars 1-3/4 but I no longer agree with that. (The irony of the Internet is that it lends credence to otherwise uninformed opinion).
If you like, you can PM me and I will be happy to share all I know (got a second? :roll:). My TBH bees were so easy this morning, I didn't use any smoke or honey (I'm out, need to harvest my Lang), nor anything and nobody got in the least bit excited as I removed and photographed all the bars, one by one. Didn't notice the queen but she may be in one of the pictures.