Sounds like you've got it sorted, Allan.
The DHE should 'cock' upright with no weight needed. The usual cause for the fly not riding right is a wing that's too long. This will tend to make the fly go over on its side. The other is as Allan says, getting floatant on the abdomen.
Years ago it became apparent that some people were having trouble getting the proportions right, primarily position and length of the deer hair wing. Hans' DHE 2.0 tying sequence makes tying the fly a doddle. It's a more conventional straight forward sequence with no tag as rib, or covering the butt ends of the wing.
Allan, I've also been surprised at how often fish will nail the DHE as it starts its swing at the end of a drift. And not just small trout. I reckon it's that disturbance and wake, which is a pretty strong trigger. I've stopped thinking of it as a fluke and use it as a tactic, especially near dark on a couple of rivers where you have to cast really long and can't avoid drag anyway.
Sandy, I think you should give snowshoe hare foot fur another go. Make sure it really is snowshoe hare, because rabbit and Brown hare feet don't have the same hair structure that the snowshoe does. As you, like CDC it's the hair structure not the 'oil' or other property that makes it float. It beats the pants off CDC, IMO, and infinitely more durable. Keep the wing sparse because it doesn't take much to keep the fly at the surface and visible. Great for those emergers under size 16.
Just FYI, This past season I conducted a little one-fly longitudinal study. Except for a couple of times nymphing the lake edges, I fished a 16 SHE (white wing, black/claret seals fur body) for three months straight, no matter what the fish were eating, including the willow grub. The tiny (size 18-24) willow grub is a real ball-breaker down here, but I caught as many WG feeders as I usually do, and as many or more than anyone I fished with this season. Most people fish specific willow grub patterns from January to April, when the trout are supposedly locked in to these wee grubs. They drive anglers crazy.
Bob