Would a dedicated sextuple or octuple shipboard Martlet launcher be beyond us these days? Tubes attached to something comparable to a Seacat launcher if, as I suspect was the case, fitting them to the 30mm mount proved problematic...
There was a test of a Martlet mounting back in 2019 - as shown in Orac's photos the missile is on 2nd Stage. I understand the long hot plume from the 1st-stage (see below) was an issue with, it is alleged, a risk of igniting the contents of 30mm ready use magazine (on T23 at least).
And anyway it is clear the denizens of the House of Darkness are looking to cut equipment funding not add new programmes. (Nothing new about parsimony towards the Navy, the Elizabethan government kept the sailors who defeated the Spanish Armada afloat as it didn't have to pay them until they came ashore.)