In the last 5 years, my city has put in at least a dozen roundabouts. I really like them, both bike and car. We have one I hate on both the bike and the car - it has 2 lanes and the inner lane MAY exit but the outer doesn't have to - that is a nightmare and I can't believe we haven't had more accidents on it. I avoid that one on the bike, or I ride right in the middle of both lanes. I don't care who that ticks off.
My take on roundabouts - they generally (always?) have suggested posted speed limits <25 mph. On a bike I take the lane, as a group of cyclists, I'd take the lane... I can easily go 15 mph on my bike through the intersection and that's what I do. Only once have I had a truck get upset with me, and I don't think he was upset, I think he was stupid. Midway through the single lane roundabout, he past me by driving up the center concrete area.
My second least favorite one is like yours - where there is a right turn lane somewhat separate from the roundabout to allow cars just turning right to not really enter it. This one isn't a problem, except the merging on the other side - but so far cars turning right have always yielded to me getting over across them before they merge into the continuing lane. This one is within a mile of my house, and I've taken it 100s of times.
I wonder instead of lobbying against it, lobby for posted bike signs and education? It would be easy to post suggested speed limits and bike signs and "bikes take lane" (or whatever would be appropriate) in the roundabout entrances?