After briefly reading through some PJI complaint threads, I've come up with a hypothetical idea to maybe fix them. I don't know if someone has already mentioned this or not, but here's my suggestions:
AFAIK, PJIs were nerfed from the betas to make superweapons easier to destroy. So this is what I propose :-
1. Limit superweapons to 1-per-system per faction.
2. Make superweapons unable to shoot to different star systems, or with at least a ridiculous 4-5 hour delay.
3. Return PJIs to the Beta 4 system, where they prevented you from going forward but allowed you to turn back.
4. Make scouts not have to spend antimatter when phase jumping.
That way superweapons would be easier to destroy and phase lanes could be strategically controlled at the same time. Now here's the counters you use to destroy superweapons despite PJI chokepoints:
TEC
The TEC faction of course, builds up their fleet to kill the enemy chokepoint fortification as usual, to try and kick down the door just as all uber-fleets of doom are designed to. They would have to build Planetary Shields and all cultural/defense fortifications available to keep them alive in the meantime. But along with their main fleet, they would build a small mini-fleet of 5-6 Arcova Scouts which are immune to PJIs with a specific tech researched. The TEC would then send their uber-fleet to crash against the uber-chokepoint, and while the battle is going on, they'd send in the Arcovas, dash through the gravwell, and jump while enemy fighters approach. Upon reaching the superweapon, they would all deploy their Timed Explosives and begin shooting the weapon, repeating the process until fighters kill them or until the weapon crumbles.
Advent
They would build their uber-fleet and attack the enemy chokepoint in an identical manner to the TEC. But instead of Arcova Scouts, they would send in their Seeker Vessels, and instead of Timed Explosives, they would use their Martyrdom suicide attacks to crush the weapon.
Vasari
They would have to use their Returning Armada and with it, they would be able to overwhelm any chokepoint in due time. Then they would just kill the PJI, send their armada in, and blast the weapon.