When I got a new Perky Pet Hummingbird Feeder a couple of years ago they changed the design by making the opening of the glass container larger. Easier to clean, but, for some reason it dripped. When I replaced the center of the flowers with the bee guards that were from my old feeder's flowers, it stopped drippng. Go figure. No idea why that happened. But, I keep the bee guards on that one.
I have two other smaller feeders, or it seems smaller, but it has a reservoir so even though the glass jar is smaller, it dumps into the reservoir and it's difficult to tell when it gets empty. That one has white flowers on top of the reservoir and they are not bee guard flowers.
All that to say I've never really had a problem with bees or other flying insects at the feeder. I'm wondering if they're looking for water rather than sugar since OP lives in a drier climate. If so, simply adding a shallow dish with water and rocks so they don't drown might be an answer.
The problem I have is ants. I now have an ant moat above my feeder. It's a really pretty clear red moat that looks rather like a vase of sorts and has a double-sided hook going through the middle. Ants come down the hook and encounter water and go back up. The bottom hook holds the feeder. The only problem is, the hook my husband put in to hang all this from is too close to the gutter and the edge of the moat is very close to the gutter and the larger ants have figured that one out. I need to add a few chain links to lower it a bit so they can't make the reach.