You have a good point there Cesarjlb, it can be remedied to some point by making a distinction between two levels, experts and novices, and have each map played by 1 expert and 2 novices (the distinction could be drawn somewhat arbitrarily, just divide the field of players into an upper 1/3 and a lower 2/3). Then you have maps of three types ENN, NEN and NNE. It doesn't seem possible to have each player play three different types, for the experts yes, not for the novices. I'm afraid that's the best that can be done, at least combinations EEE and NNN can be avoided by such a system. Moreover, it depends heavily on the map what type would be preferred over the others, so yes, there is some advantage, but there is no telling how large the effect will be. It could be assessed by looking at the scores of each type separately in hindsight, and if the difference is significant, a correction could be in order.
With 2 experts and 4 novices the games could be
E1N1N2
E2N3N4
N1E2N3
N4E1N1
N3N2E2
N2N4E1
Two novices never participate in two different maps as a pair, both experts play maps of each type, but some novices play maps of the same type
N1 has ENN, NEN and NEN
N2 has ENN, NNE and NNE
If NNE is preferred over NEN, which could be seen from the scores of the two types, N2 has an advantage over N1, but the advantage can be quantified. Can it really; N1 participated in both the NEN maps, so the effect of the low score can be addressed to N1, as well as to the map type. By comparing the results of N1 and N2 on the ENN maps that could be established, but the problem is they played in the same ENN map. Who can come up with a "fair" schedule, with internal corrections? For more players it may not be such a tie.
Thank you WinterPharaoh for an interesting challenge!