Your points are kinda contradicting each other. You want the ships to have an easier time vs fighters but at the same time you want to make them smaller. Which isn't just a cosmetic change as you said, it's a balance one too, and a big one. The whole point of fighters having current size is so they can be hit with ship weapons easily. If they were smaller only beams would be able to hit them, or you'd need to rebalance every single weapon in the game which isn't happening.
They're not mutually exclusive.
I find Fighters' size too large too, since they can easily block missiles and heavy munitions not meant for them, often enough for it to be frustrating. Making them smaller makes them harder to hit, yes, but it also makes them less of an obstacle in firing at full-size ships. Depending on the degree of size reduction, this could balance out the suggested PD friendly-ship bypass and what I'm about to add.
A balance pass will need to be done at some point prior to full release, and it might be worth the effort if it mitigates the effectiveness of fighter swarms without nerfing them into oblivion. It also addresses the disbelievability of fighters attacking targets from behind another, yet the target not being able to hit back for risk of FF or otherwise wasting shots on wrecks, terrain etc.
With fighters vs full-size ships, I'd like further changes on top of those suggested in OP:
Projectiles from large weapons punch-through fighters, dealing the projectile's full damage to the fighter but continuing on to hit what was behind.
IPDAI allows Medium weapons to bypass friendly ships when targeting fighters
Fighters deal reduced damage to full-size ships except dedicated anti-"capital" weapons - Ie. bombs, torpedoes and gunship "primary" armaments.
