So the firing delay and extra module mean that PDs takes up more room and are less effective against missiles. Thus making it harder to fit PD on small ships, and making it harder to counter them at close range. This will make kiting less desirable, and make missiles more of an anti-ship-swarm weapon. But, there will still be a missile/anti-missile arms race.
Missiles will be better vs swarms and better vs big ships with lots of PD. All the missile ships will need to do is get in close to counter the PD before it can target. If the big ship has lots of close range weapons with higher DPS than the missile ship, then the M ship simply kites it. If the big ship has higher close range DPS than the M ship AND a significant PD defence, then its back to the arms race and the same old problem.
Problems will be worse
I think this step is part-way to a solution but it's actually going to make things worse. Small ships (which are struggling anyway to stay relevant) are going to be less useful still. Plus the old problem of M>DPS>PD>M turns into something worse M>DPS>PD + M>PD. Plus a mixed ship of DPS+PD is still going to struggle in close and long range vs Missile swarm ships.
Solution - Specific missile role & Flak
If you want missiles as an anti-ship-swarm weapon, and want them to remain a little useful in big ship battles too, then a dedicated anti-missile-swarm weapon that mainly protects bigger ships is necessary. If the anti-missile weapons can be designed so that they're imperfect and the occasional missile can get through then all the better.
PD could still be useful in an anti-missile role for small ships, vs individual missiles. But it would need nerfing a bit, maybe make it slightly less powerful or less accurate or slower firing, so that it struggles 1v1 vs missiles. It would mean that small ships would not be defenceless against missiles, but would still be very vulnerable to them
One idea for an anti-missile-swam weapon is to give Cannons Flak ammunition that can target ships and missiles. Flak projectiles would be faster and would detonate in the proximity of their targets rather than on impact, they would then have an AOE that would damage or destroy all missiles in the AOE, and do low damage to all ship components caught in the AOE too.
With a short range and (relatively) slow RoF, Flak would provide a strong defence against missile swarms for large ships, (which could mount 3+ cannons + PD for each direction) but would be less effective on small ships.
Flak could be added with alternate ammo or with a separate weapon altogether (2x1 or bigger), and would still be able to target ships as well as missiles but have zero penetration and low AOE damage.