Detrak optimal score

Detrak is a fun roll and write game. Every turn you throw a pair of dice to generate two symbols at random. The goal is the score points by placing symbols on a grid. The more adjacent symbols there are, the more points you score.

The question I'm looking to answer here is:

What is the highest possible score if the sequence of symbols is known in advance?

I haven't found a smart answer yet. The brute-force way I see is to list all the possible grid layouts, and then evaluate each layout:

• precompute_scores.py generates a .json file mapping each possible row/column/diagonal symbol combination to a score
• enumerate_layouts.py generates a .txt file with all the possible grid layouts thanks to backtracking
• evaluate_sequence.py calculates the best possible score for a given sequence of symbols

Each script has an N parameter which can be changed. I haven't managed to run enumerate_layouts.py with N=5 because it's simply taking too long.