You guys do realize that there are more than a few folks on here who have built BHS hubs + CX Ray + 340 rims and have been riding them for 1,000's of kms already, right?
Yes, and I've heard lots of complaints from several of them. I am currently riding a 340 on the front, 28H 2X. I built it last year and has held up fine. As an amateur wheel builder I put alot of time into my builds, so verification from the 195 lb OP is the best verification I can find if the mis-matched tensions of the BHS rear hub mate to the low tension 340 rim. My guess is that if built with care, it will hold up fine.
I have the exact same hubs, spokes, 24/28, alloy nipples but laced to Nio30's. They roll really nice when up to speed, very fast and smooth feeling. I have the exact same lacing, rim, spoke/spoke count, nipple configuration but laced to Tune Mig 70/Mag 180. Both wheels feel stiff laterally, I am 170 and mash big gears.
The biggest issue I have with the BHS hubs (I am assuming it is a hub issue considering all other things being equal to my Tune built wheels), is that they accelerate nicely in low climbing gears but if I am cruising along at say 23mph and apply pedal force to increase speed, they feel sluggish initially but ok a few strokes later. Annoying more than anything. My Tune don't suffer this effect at all, maybe it is the Tune bearings that are the difference. I have some old Real-Design Supersonics, they are better than the BHS hubs in this regard even though the rims are heavier. Not sure what the deal is but I am happy with the BHS wheels as my back up/rain/crit wheels.