I've had decent-ish results with the Chusi Gandruk barley from the Kusa seed society's site (note, Salt Spring has acquired a lot of their seeds and are offering them individually [instead of the pre-selected multipacks Kusa does, so people might do better there). It grew pretty well for me and I got a decent amount of grain back (unfortunately, something like 99% of the grain I harvested disappeared at some point (maybe it got thrown out with the trash) so I don't have any to share myself.)
It's pretty resilient, and the gene base is VERY wide (and don't worry about the "seven feet tall" thing, they don't get that big here.) In fact, it is SO wide that you basically have to evaluate the stuff on a head by head basis.
My usual problem with grains isn't so much the wet and mold as the insects. By the time they are ripe, nearly all types of grain I grow have been so ravaged by aphids and other plant suckers that the amount of good grain is minimal, and, more importantly to me, the heads have become rather ugly (that's important to me because, as I know I will NEVER be able to grow enough of any grain to make a meal of it (I just don't have the land space) most of my grain is destined for use in dried flower arrangements, so I need nice, clean, well shaped heads. Kusa's einkorn and two emmers* did pretty well, but that has been about it for true wheat (and I had such hopes for the shot wheat).
*Technically three, as the einkorn Kusa sells has a small amount of seeds that have naturally doubled their n over the years, and when an einkorn doubles it's n, it becomes an emmer, by definition.