Sure, the enclosure reduction will make an audible difference and provide a stronger upper bass. The bass will sound a little more 'live'. However, the parameters on that woofer should still work well in 1.3 cu.ft. gross.
Those 12s will 'hit' with ease and two 12s properly powered should be a monster. If those two 12s aren't more than satisfactory in the recommended enclosure then start looking at the location, tuning (crossover selection & gain), and other aspects of the system.
Btw, quality bass also depends on having enough midbass from your coaxials to create a good balance. When I hear the term "boomy" related to a larger woofer, I don't think the woofer is too large, I instantly think the sub gain is too high.
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