It also came with CRC magenta front tires and Yellow rears (3 pairs of each). Are these a good starting point for tire compounds for medium traction carpet and 13.5 blinky?
These two different tires are from different families of rubber which could pose an issue. What I mean by this is that they generate different amounts of grip, the yellows are a tire that is generally considered a stock tire because it is very free in the corners and without a ton of grip. The magenta's on the other hand is a more aggressive tire that is going to generate a lot of grip. In my experience the magenta could possibly overpower the yellow rears.
One thing to try would be to get some chrome fronts to go with the yellow fronts and some green rears to go with the magenta fronts. That is more natural pairings for those tires and would give you different options that you could test and determine what works best for you.