Did you build a working calibration strip for the drum? Perhaps surprisingly this puzzle is related to the problem of assembling a DNA sequence from partial fragments and the same idea you can use to solve it underpins genome sequencing software.
For those of you impatient to get to the solution, here is one sequence that works:
Solution
RAARAGR GARGGAAAGAGGGRRRARRG
Of course, it is one thing to find a solution, but an entirely different thing to build a method for solving this type of problem. The secret is to use something called the De Bruijn graph. This is a network which, in this case has nodes labelled by all the possible triples of the letters R,A,G, so it has 27 of them. There is an oriented edge labelled UVW joining two nodes UV to VW (where U,V,W are each one of the letters) and you can think of traversing that edge as spelling out the word UVW. The solution we gave above defines a path through this network crossing the edges RAA, AAR, ARA, RAG and so on in that order. It is easy to see that the network has exactly one edge for each possible triple, so this path crosses every edge exactly once. The problem of constructing a calibration strip is exactly the problem of finding a path through the network which crosses every edge exactly once! From that point of view we can see that it is not unrelated to the problem in our previous Sunday Puzzle, which is maybe a little surprising.
The relationship with genome sequencing is that the sequencer splits long strands of DNA into subsequences and then tries to figure out how they are reassembled into the original strand of DNA. For that it uses a De Bruijn graph with an alphabet of 4 letters,:A, C, G, T, which stand for the four possible bases that appear along a DNA strand.