A few ideas about research that might help the balance.

Unfortunately, there has never been alterations to the tech trees except in expansion packs.  So, sad to say, this discussion is purely academic.

This would definitely bring phase missiles into line in the early-game.  It would still be the best upgrade line because the units it affects complement each other very well, and because its levels are actually very low by the standards of other comparable paths (PM's are 1/3/5/6 compared to TEC's missile 2/4/6 and Advent's beam 3/4/6).  However, it would no longer be overwhelmingly powerful.

Unfortunately, there are two big flaws with this.  The first is that it does nothing to deal with the late-game implications of phase missiles.  This would only worsen their current issue of disproportionately affecting Advent (since Vasari vs TEC may never even reach shield bypass) and balance-wise we may as well take the next logical step and remove the feature entirely, which brings me to my second point.  This is one of Vasari's central "flavour" items, and this change would strip them of it and makie them wait to the late game to get it.  While that may help balance (essentially by bringing homogeniety), it would reduce the depth of the game in the process.

I agree with the flaws you stated. What's been kind of killing my love for Advent is also exactly what you mentioned: it seems like Phase Missiles are especially engineered to destroy Advent. This isn't necessarily bad or implausible, but I'd think Advent would engineer something to counter this vulnerability.

I was thinking: Guardians project a shield. If we think of it as an actual shield as in some of the incoming weapons fire collide with it, then it could act as a first line of defense against Phase Missiles also. Fully upgraded, I think a phase missile has a 20% chance of bypassing shields, right? So, any given phase missile fired to the protected unit would have a 20% chance to bypass the guardian's shields, and another 20% chance to bypass the actual ship's shields. This would bring a protected unit's phase missile bypass chance at 4%.

So, maybe modifying the shield projection so that it also adds a bit of phase missile block could be an ok idea?

Another completely different idea here: I read a post of yours some time ago, and I agree with you when you said the main problem is focus fire and how capitals ships cannot hold the front lines after a while. Simply changing modifiers would not do the trick, as there will be always a sufficient force to pop a capital before it does anything worthwhile.

So, I think we can tweak how a capital ship scales with levels. I was thinking: can we make it so that a capital ship will have roughly the same survivability and firepower compared to a fleet at any given point in the game? Let's say a capital ship level 1 is usually found when you have 5 LF and 5 LRM. At this point, a capital ship can dish out lets say 15% of this fleets' damage, and can sustain a minute of focused fire from this fleet. Can we make it so that as our fleets grow and capital ships level up, the scaling is done in such a way where the capital ship will always have 15% firepower of it's fleet and sustain roughly a minute of focus fire from such a fleet? (Numbers up for debate, of course)

So a level 1 capital ship is as it is, then:

Cap ship reaches level 3 around the time where you have 10 LF, 15LRM, 8 flak and 2 carriers. So, the cap ship gained enough HP/armor to still withstand a minute of punishment from all those, and has upgraded weapons which can roughly dish out 15% of their damage.

A level 6 cap ship is around when you have maybe 30LRM, 10 carriers, 15 flak, 10 heavy cruisers. No worries! During the past three levels the cap ship increased enough in survivability to still tank a minute of focused punishment, and can still dish out respectable damage compared to the entire fleet.

Now, I know I didn't take having multiple caps into consideration, but with a scaling like this they would still work if you keep cap ship numbers low. This would discourage getting many cap ships as you want them to level, but would still make them quite powerful and not lose their power at any point in the game.

Agreed; the more I consider it, the more I'm certain Advent (and TEC, for that matter) really need new cruiser abilities to patch the respective holes in their late-game.  Unfortunately, I don't believe the Guardian is the right unit to target.  Its repulsion ability already is Advent's best non-shield related gimmicks.  If anything, I'd give an ability to the underused Domina.  I also don't think an ability that simply disables (or reduces) phase missile success chance is the right approach; the problem right now is an ability that is basically custom-designed to negate a specific faction's core advantage, and this is just another such ability.  I'd rather have something more strategically meaningful.

Unfortunately, capital ship level is a bit of a wild-card.  It basically comes down to a matter of fleet mortality and capital ship mortality.  It's entirely possible to have situations with relatively small fleets with very high-level capital ships, or very large fleets with very low-level capital ships.  Militia makes it even worse; it's feasible with a good militia layout to be level 5 and still be in an early-game scenario.  I don't think this is feasible.

Recently, I've been leaning towards the move-speed solution.  Give capital ships faster move speed so they can disengage other frigate types at their discretion.  This means capital ships can still be killed by strong combat frigates, but now have the ability to avoid them.  By tweaking each class of capital ship differently, we can also streamline some of the imbalances between them, for instance making carriers slower to account for the fact that they're presently the strongest type of capital ship.

The one thing i love about sins is the fact the each factions are in anyway similar to each other. It would make sense for the damage upgrade to come first and then the modifiers afterwards but you encounter a problem.

Phase missiles bypass shields is enough already. The amount of damage is a non issue due to the part where the actual missile hits the hull. That already is an advantage. Most vasari ships have phase missiles, that said damage increase is not a issue until late game thus why the tec tree is fine the way it is.