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Well done! It has great potential as perhaps a string quartet.

As already explained clearly by the others, tremolo is not a specific division in time, so that point has been covered. Assuming therefore that what you do want is the specific precise time-division you refer to, you do not wish to "switch to 12/8". However, as you have worked out, 4/4 and 12/8 are closely related, by exactly this division into triplets, and it's a common thing. Likewise with, for instance, 3/4 and 9/8. Often you will need to make a choice between whether to base your tempo marking on the base time interval, or the dotted one (dotted means one and a half, so 3/2, which corresponds to the inverse ratio of 2/3 for triplets). You need to mark your triplets. If you want to save on writing, you can mark a section sim. (simile).