Lars, I do think it would be worth a try since you already have the CL33. One thing I have found out in 66 years as a ham is that sometimes antennas work much better or worse than you expect. As suggested, you could just put up the driven element first to get a rough idea if there is any chance of success. The driven element alone will probably have a higher Z than the Yagi, but for a RX test do not worry about that or adjusting the element. If it looks like it might work, then try TX, possibly at low power if the SWR is high. A Yagi has nulls in various directions, and RX noise may be your biggest problem, but even rotating the antenna 10 degrees may null out nasty noise from a neighboring house. If it seems to work, and you need a little more room to rotate, possibly the Yagi would still work OK if you bent the elements down say 10 to 30 degrees perhaps 2 or 3 feet out from the center, so each element would be a flat top inverted V. You could possibly just replace a section of each element with piece of bent aluminum. You can eliminate SMPS and other noise in your house with some ferrite and effort, but who knows about neighborhood sources. Often, but not always, noise is much worse on 160, 80, and 40, than on 20 through 10 meters. The Hex beam idea may be the way to go, but experimenting with the Mosley first may save some money. Try to keep the ends of the elements as far away as possible from the structure (I know this is impossible). Plan on spending some time in the attic, since much adjustment may be required on this multiband antenna, and the structure may detune it so much that it would be nearly impossible to get all three elements tuned correctly on all bands. Another idea you could consider, build it up as a two element Yagi. Adjust the driven element. Then adjust the reflector for minimum signal off the back. This adjustment often will get you very close to the maximum forward gain, but is much easier to do than tuning for best forward gain. Probably a test signal as close as 50 feet would even work.
No guarantees that any of these things will work, but these are just a few of many ideas to think about. Good Luck, Rick KL7CW