You could also try one of the paste solutions- CrOx on balsa or fabric (I wouldn't recommend pasting the fabric on your only strop, though). There are threads on making your own; just do a search. Or, you could go to whipped dog and order his poor man's strop kit; it comes with a small leather strop and a piece of balsa charged with CrOx on one side and IrOx on the other. I have this kit, and while I don't really use the strop due to its small size and lack of fabric (it is quite handy for quick out-of-town trips), I find the pasted balsa to be really helpful.

I also have very thick individual beard hairs, and I've already gone through periods of wondering how much it effects the longevity of my edges. My experience seems to indicate, so far, that improved beard prep and improved stropping technique have more to do with edge longevity than beard type (except that these thick hairs may need more thorough prep- YMMV).

+1 on the advice above- try an extra long stropping session (perhaps put the strop on a counter or table to eliminate variables of pressure and strop tension). If that doesn't work, consider whipped dog's kit or a similar DIY solution; also, check out Lynn's video on blade maintenance. Good Luck!