While I believe everyone is unanimous in their agreement that the Warscore needs work, I believe what we need is both a semi reworked Warscore as well as a much more influential influence system tied directly to warfare.
Honestly the warscore system seems fine to me in theory, tallying each and every battle and action to see their worth and play them against one another to artificially determine who is -winning- in a form of galactic politics. The problem I feel is how the game tallies and how limited your actions really are during it all. On one hand I feel like loosing to a bunch of raids and such from multiple armies should be a no brainer, but I also agree with the OP that if he was so gosh darn powerful comparatively, then their attempts at making him lose because of an artificial influence shenanigans is a bit contrived. The game needs a way to alter war goals, make war goals actually influence the outcomes more, give more and varied ways to fight said wars as well as have ways to knock an opponent out of the fight when dealing with a multi-war.
I really like the influence currency as a great way of expressing how much your race agrees or doesn't agree with your actions, as well as the pressures placed upon or assisting your governments in this task. I feel that wars need to be tied to this or at the very least derived from while also using warscore as a way of helping sway said politics.
*When you start a war, your current Influence should be copied over to a war influence (depending on your faction types you may see a negative or positive to your starting total)
*This influence can be spent on say, I dunno, hiring mercs, buying ships for your allies, changing/adding/subtracting your wargoals, using spies to check out enemy systems ahead of time.
*Wargoals should matter. For every month you haven't attained your wargoal, you lose influence, however succeeding gives you a sudden instant huge boon. Defending a wargoal nets you a positive each month but a massive decrease if you fail (at least until recaptured)
*Ceding planets should only matter on the ones you captured, while liberating can be any (Except homeworld) Homeworlds should also not be able to be ceded but can be made a vassal. (Vassal should only be possible if enemy fleet is taken down to 5 or 10% or whatever % of your own fleet, or you managed to capture their homeworld)
*Destroying mining/research Stations should have an increasing warscore cost based on the % versus remaining stations. That way even enough raiding of planets and even stations could be seen as taking out enough resources as to make warfare unprofitable. (Materialistic races may be affected more than others for example)
*Capturing sector worlds, vs core worlds, vs homeworlds, vs wargoal worlds should also see a varying level of warscore points differences. Generally sector worlds are already the ones you don't care about as much or are slaver worlds and such. (Individualistic empires may care a lot more though since all are precious.)
*Another major one is armies in general. Depending on the population of the enemy homeworld, you should have to leave a certain level of army strength nearby to keep it going. However depending on the type of army should change some outcomes. High moral damage would see the world go quiet and the enemy loses influence faster. High martial damage could see less force actually required in general to hold it. Where as the more dangerous ones like xenomorphs, titans and even mindless robots may see full on structure damage or population purges!
*Lastly, the reason I'd like to see a war based influence tally be separate is because I feel it should be affected the most. Have a bigger fleet than your enemies, gain war influence! Be a warlike race and war is still going on, who cares, war is great! No matter what, war still costs resources so the longer it goes, the higher the cost for everyone. Your warscore not looking too hot, people are starting to lose faith so down it goes. Warscore looking good even though your fleet is pathetic, well at least the people have some hope! Got those wargoals you set out for, good, here's some more influence! The idea being that even if your warscore isn't looking too hot, you can always find ways to fight back or help your allies. On the flip side, perhaps you could spend said influence to force a battle surrender based on warscore difference between you and your opponent. A battle surrender would mean they are effectively out of the fight when it comes to war on multiple factions. Forcing a faction to surrender would be a huge warscore boost, making the next few factions much likelier to surrender or stop fighting as well.
Anyway that was probably too long and no one will read but I would like to see a much more in depth take on warfare in general because it's definitely a sore spot in the game right now. While the OP should have been watching his warscore and I like that he was beaten out by hit and runs and raids, the fact that he was taken out when he could have just turned around and stomped them shows the game is too limited/doesn't differentiate enough between what is actually a lose and what is still strongly in someone's favor.