I'm afraid that doesn't work. Imagine that you did find p-2 and p+18 prime. So you have a septuplet. But, you started from a sextuple so p+12 is also prime. This means that your septuple is also an octuple: it has 8 primes in the range p-2 to p+18. A difference of 20. But Athony Forbes tells us that the minimum distance possible for 8-tuples is 26, so the 8-tuple with distance 20 cannot exist. But we said it did... this absurd comes from assuming you could find p-2 and p+18 both prime.
So the test is needs to include a "p4 or p12 not prime" test as well.
Sorry for any false hope!
Regards,
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bsunau7