Today I replaced the opamps with the new ones I just got from Analog Devices. These were SMT parts and I had to solder them to DIP adapters. But they share the same pin outs as a DIP, so the substitution was trivial. They work like a charm. I have now started to work on the mechanicals. I made a platform to hold a servo, and the slip rings. I built a wooden pulley and added the black white pattern for an optical index sensor. Once connected, I ran a test to see how much noise the slip rings would introduce. From the scope traces, I would say less than the noise floor of the power supply I was using. So far so good.
At this point I realized that not all the electronics can live on the rotating or on the stationary platform. The circuit I made needs to be split into parts. I wanted to put all the analog circuity as close to the photodiode as possible, but this would have meant the SPI controlled digital pots would have had to be on the rotation platform. That in turn would have meant more signals on the slip rings than I have rings. So the new design puts the first stage opamps by the sensor and the analog signal will pass through using two slip rings to reduce noise. I spent the rest of the day splitting the circuit and retesting the design. It would appear that this will work out.
Next step is to actually wire a small circuit board (rather than a breadboard) for the radar head. Then I can take this whole mess outside and see if it has any chance at working.