This is exactly the reason that I have bought an ASA DDM60 raymo
Should be arriving within the next month I hope! It does however not fall into the price range of the amateur market which is what you're looking for.
The next closest one I can think of is the 10 Micron mounts, these are virtually the same price as the DDM60 (for the same size). What allows both of these systems to work is closed loop absolute encoders, these on their own are very expensive items.
The difficulty comes from the fact that even if you have a "perfect" polar alignment, it doesn't work for every point in the sky due to the refractive index of the atmosphere. If you use any of the Bisque (Paramount) mounts, they can counteract some of this via T-Point with sufficiently large sky models.
One mount that has very little Periodic Error is the Friction Mount such as a Mesu 200.
http://www.mesu-optics.nl/mesu200_en.html
They fall into the medium price bracket and to some extent, do not have any gear system so they have a small error but it isn't periodic as such. Due to their size, very smooth curve which is very easy to guide out.
One of the problems that amateurs have is cost, to get something cheaply it has to be mass produced and there in lies one of the major issues. As a manufacturer you can make a LOT of parts at pretty good tolerances at a good price... OR you can make a small number of very high quality ones.