I had limited time to develop and test the long-term campaign progression for the Templars, so you're essentially the first one to actually test it out; I am grateful you made such a detailed report, since otherwise I could only guess how the experience is.
That's surprising, since pretty much everything else other than the stuff I mentioned seems to work and meld so well with the campaign, and even the issues I mentioned are mostly quality-of-life stuff. Definitely nothing game breaking.
The only thing I'd really call gamebreaking about the templar integration into campaign would be the fact that the player's accumulated perks from character levels will eventually make them capable of taking any templar threat on with minimal risk, even with vanilla ships, though I suspect that it's more of an issue with the synergy some character skills have with certain vanilla ships in particular.
For example, the metric I usually use for weighing the challenge of campaign content at a late-game level is reaching a high enough character level to get level 10 ranks in all of the stuff that directly improves ordnance points and combat capability, and kitting out a single paragon with a few choice loadouts of vanilla weaponry (all beam weapons or all pulse laser weapons), and seeing how autopilot fares against the biggest and baddest threats.
A fully leveled beam paragon with all the best hull mods and combat perks like this is able to take on a templar fleet of pretty much any size, even multiple paladins simultaneously which are supported by jesuits and bulwarks, without sustaining any hull damage at all unless the autopilot AI pulls a significantly stupid move. When player controlled, it's not only possible, but actually quite easy to win against the best the templars have to offer without even taking armor damage. The carrier and fighters are especially susceptible to the amount of extended range beam weapons a paragon can carry. This is with SS+ mod as well, though, for what that's worth, and I'm talking about character level 30-40ish worth of upgrades, and specifically the paragon, which has somewhat unique advantages that work well with the 30% hard flux dissipation with shield active perk and general flux capacity/dissipation bonuses.
Amusingly, the vanilla beam weapons are actually more effective when stacked onto a paragon than trying to add in the stronger templar beam weapons, since the lower constant flux costs of vanilla beams allow for constant suppressing fire even while tanking hits on the shield.
Relatedly, and of possible interest, is that the arondight accelerator's flux damage when hitting a shield seems to ignore the fortress shield shipsystem's damage reduction. This might also be the case with the secace autocannon and Galatine Heavy Disruptor, I suspect, though I've only confirmed it with the accelerator. I figured it might not be intentional, but if it is, it's pretty much the only thing to give the abovementioned high level paragon setup any real trouble.
Sorry for the long winded, rambling walls of text, and thanks for your quick response and excellent mod work!