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The non-trivial score each robot achieves (attempts to achieve) by executing these compulsories would be carried into each qualifying or elimination match/alliance by the robot/team and would be added to the alliance score achieved during each match.
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I like this idea: It allows for some pretty complex and varied autonomous modes without extending the length of the individual autonomous matches. You could have a 2-minute long autonomous qualifying period once in a competition, and all the qualifying matches would remain the same length.
As an extension to your idea, I propose that teams could have a small number of retries throughout the competition, with their highest score so far achieved (not the average) being the value that is carried into the match. They still get an advantage if they come into the competition with a ready-done autonomous mode, but if they fail initially due to equipment failure or unforeseen bugs, they can try again with the penalty of playing some qualification matches without the advantage.
In a one-day competition, teams could try once before qualifying, once at a mid-competition break, and once just before eliminations. Since drivers do not have to actually actively do this, the trials could be done by a volunteer on a seperate field whenever the team is ready.