The cheap chinese engine from HF may be a Honda knock off, but it wouldn't be a Honda. They may have made it so some Honda parts interchange. if you don't want patronize the Chinese knock off industry (I don't) you can find old front tine rototillers with functioning engines on craigslist that will match up, but check the bolt pattern and shaft size/type closely. Many of those will match up with the throttle cable as well. I would rather money in a local person's pocket who is clearing out their garage than the Chinese. Whatever engine you put on, make sure you check the oil with the engine level per manufacture's recommendation. The way a Troy Bilt sits, it has the engine at quite an angle, particularly if the depth is set to till deep. Tecumseh engines had their oil fill tube to the rear and if you checked the oil without leveling the engine or at least setting the depth to shallow, you could be way too low on oil even if the oil level indicated normal. I think running low on oil is what attributed to many Tecumseh Troy Bilts throwing rods. Again, this will apply to any engine you install. If the fill tube is to the front, you could add too much oil which can be bad as well.
Many name brand manufactures now have engines made in china now to exact standards. This doesn't apply to knock offs.