Is it not possible for you to get a simple trapped dipole up about 32-36 feet?
1. A dipole is bidirectional, with all of the gain broadside to the dipole. There are nulls, in some cases heavy nulls. So unless you have a specific place you want to point it stationary, or unless you have a rotator [mechanical or armstrong], this might not be a solution.
2. A dipole is going to have significantly more gain than any vertical you are likely to build IF you can get it up at least a half wavelength. At a half wavelength height (16-18 feet), it'll do pretty good on DX, but it won't be a long haul performer. Get it up to a wavelength (32-36 feet), and it'll beat a vertical any day, by a large margin, for signals broadside to the dipole.
You could make a trap/coil to give you 10m / 12m. That won't get you 11m, but if you've got 10m and 12m [at least at the peak of the cycle] you'll have plenty to work without dealing with 11m.
Of course, you could always use an antenna tuner [which will likely give you a little loss] to tune 11m if that's a must for you.
Anyway, if you can stick something the size of two fishing poles separated by a T, horizontal, at 32-36 feet, you'd be having a helluva lot of fun chasing DX. And you don't need anything thick. Build one out of fishing rods. Or get some nice small fiberglass tubing [
http://www.mgs4u.com ].
If you can't put a dipole up at any height, then forget what I said. Remember though, a 10/12m dipole is going to be extremely light and isn't going to create any kind of appreciable windload on whatever kind of mast you stick it on.
mike
PS: My gain claims are vs a 1/4w vertical. You're talking about a 5/8w dipole, and I'm not sure about gain figures. But I'm fairly certain that no matter how you slice it, if you can get the height and can deal with the bidirectional nature of the dipole, it'll be a better performer than the vertical -- and will not be quite the eyesore that a multielement vertical may be [if you have neighbors who are pains in the ***].