I've never run the Mini on carpet a friend back East did and used most of the same set-up just Foam tires.

As far as insert I use a Tamiya 24mm insert first then a 50d shaped insert inside that the diameter is just a hair smaller than the HPI. You might also try the Yokomo thin inserts as they are a touch thinner than the Tamiya's. I also use the black shaped 50D insert for the rear it leaves a nice air gap and awesome grip but does groove the inner part of the tire over time.