A good cop out is to go about buying technologies from other civilizations to get rid of their economic problems. The most important would be stock markets, but anything that provided economic bonuses that could be mass produced would help. The intent is to be able to fill your empty tiles with something other than charging stocks to make money. You also want morale buildings (or just morale bonuses) to better control the morale of your worlds. Morale will help you to raise your tax rate.

Another thing you can do is to put a priority on nabbing galactic resources. The ones most worth while getting as the Yor are economic, morale, and influence. Economic will offer a bonus to your tax income. Morale will allow you to raise taxes. Influence will offer tourism income (determined by the population of galaxy and what percent of area of influence you control) and will the area that your super ability affects. The Yor need to research their factory techs to unlock more mining modules, but all of them together they will only give you a +30 bonus, instead of +39 that you could get with the Terrans or other common civilization. The other galactic resources are helpful as well. Research will improve research output, so you can opt to have less research buildings and still remain competitive, or increase output and put yourself far enough ahead so what few ships you have can overwhelm your opposition. Military will obviously boost your ships to better help you overwhelm your opposition while needing fewer ships.

Get far ahead in research. The Yor have research advantages because they get a research matrix (a low maintenance research building) at the start, and many of their early research buildings can be researched quickly, and they have other research bonuses. Being several generations ahead in research can provide you with weapons and defenses that can make you nearly invulnerable to enemy opposition. With some work, a bunch of lone big ships should be able to harass the enemy on multiple fronts, preventing them from attacking you and opening the way for your troop transports.

You will likely need to adopt a Zerg rush mentality. The Yor don't have the things they need to compete well economically in the long run (which will hurt everything else you do), so you will need to attack early and take worlds before the enemy can stabilize. A number of Yor advantages allows the Yor to stabilize new world quickly. The Yor get economic bonuses and population growth bonuses which will make recently conquered worlds useful quickly. The Yor also get a number of planet improvements (1 per planet), that can be built quickly and have little maintenance.

There are gaps in the tech trees. Some of them did get patched before Stardock stopped updating GalCiv 2. I don't know them all off-hand, but I do have some examples though.

The Thalans once lacked the "Space Weapons" tech, which unlocks a starbase module that is the prerequisite for most modules that starbases get for personal defense. Not only is it a prerequisite for a number of common starbase defense modules, it is also the prerequisite for the unique Thalan starbase defense modules. This was one of those gaps that did get patched.

The Drengin (and to an extent, the Korath) get population growth bonuses for all farming techs and the final also provides a morale bonus as well. Their version of the prerequisite tech for the Tech Capital gives a +5% bonus to research. Things like that is why I often try to buy those technologies from the Drengin instead of trying research them myself (unless I am the Drengin). Also, one of the Drengin slave pit techs gives a +5% bonus to social production, while the Korath version doesn't, so things aren't always consistent.

For a time, some of the civilizations didn't get all the mining and production assist modules. Those were tied to the standard factory techs, and since civilizations that got alternate factory techs didn't get those techs, they didn't get those starbase modules either. This is one of those gaps that did get patched, so most civilizations get such starbase modules with their factory techs (however, I recall that the Drengin can find theirs after advanced starbases).

The Yor get something to replace the Manufacturing Capital, but it is expensive to maintain, and its bonus (+50%). This is duplicated by the Iconians as a planet improvement, which is also much cheaper, and is one per planet instead of a Super Project.

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Yes, many of the unique civilizations appear to lack a number of Super Projects, Galactic Achievements, and Trade Goods. Its not only that they don't get the stuff available to common civilizations, they also don't often get anything to replace them.

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I believe that some of these problems exist due to Stardock not being aware of the problems (or at least of them). This isn't the first time this has happened. Starbases defenses didn't get updated throughout the patches. They are more or less the same as they were back during initial release. In fact, because the combat has gone through some revisions, they are worse off now (they still can only kill one ship per turn, now enemy weapons can weaken their defenses, and ship hulls are even larger). I'm fairly sure they still have the same modules and the same stats as they always had. The prerequisite techs may have changed (especially during TA expansion), but this was not always for the better. The only real improvement they have got is that constructors now get starbase repair kits.