Another budget contender is Federal rsrr.
Just to simply things.
Yokohama A050, Hankook z221, nankang ar1, dunlop dz03, nitto nt01, toyo r888 etc. are proper r spec track only tyres. Some are road legal but you would only use them to drive to and from the track.
Yokohama Ad08r, Hankook rs3/4, nankang n2r, federal rsrr etc. are more street oriented motorsport tyres, not true r spec semi slicks.
Any of the above will serve your purpose well, the r spec will give you a fair bit more grip. Since you have spare wheels, i would be going with the cheapest r spec i could get my hands on.
There could be an advantage using the non r specs, if you don't end up doing as much track work as originally planned, they could always be put to use as street tyres.
Good luck with your deliberations.