I too, wear a DUI harness with my BP/W combo when diving dry. I was ecstatic to get rid of a weight belt! Nothing hurt more than doing a week of cold water diving and having lead block weight on your hip bones. My hips pointers would be bruised by the end of the week just from the weight.
I have hip burisitis now, a new development since I got my DUI harness back in 2001. I was teaching this past Saturday, all day, and was wearing a wetsuit in the pool. I get cold easily, especially in the pool all day with little movement. I geared up and as soon as I plopped that weight belt on my hips, the discomfort started.
I have the stiffer webbed DUI harness, and have not had any experience with the softer strapped version. The straps do not interfere negatively with the BP harness in my opinion.....all you need is a few extra seconds to sit both where you want them before you stand up fully bearing the weight.
When you first get the harness, if you get the stiffer one, you will have 30 minutes to an hour or so of fitting. Have a friend do it for you. I wore the harness and my dive buddy cinched and tweaked leaving just enough slack to allow for the drysuit. We added a little weight to the harness and he fine-tuned a bit further. It's a rather slow process with the webbing and the buckles, but well worth it as once it's tweaked, it's set for life. He's a bit of a perfectionist, so it may not take you that long. He actually marked with chalk, shifted, tried on, marked again....you get the idea. But it sure fits perfectly, right below my waist belt of my BP harness. Since the rings are the dump mechanism, you can put the crotch strap over or under the harness, whichever is easier.