However most naval targets would have RCS of 200m^2 plus so detection range would not be an issue... curvature of the earth would have more influence on range than anything else.
The original R-33 can hit targets at 120km so I rather suspect the tracking range is greater as the R-33S can engage targets to 150km and the soon to be introduced if not already introduced R-37M will have a range of 300km.
If you want a platform to carry long range anti ship missiles then right now I would say use Tu-22M3Ms, and in 10 years time I would say the PAK DA would be ideal for that role too.
The Mig-31 is an excellent interceptor... there is no need to make it anything else.