Oh I don't have any trouble at all protecting my starbases when I have ships around. That was kind of my point - I didn't have anything to defend them with since I heavily invested in starbases before military buildup.
(The idea was to benefit from the production/research over a longer period of time instead of 'wasting' it building a fleet in a time of peace that im just going to rebuild/upgrade later anyway - Pirates kinda taught me the error of my ways here - be prepared for blazing electric death at all times)
I find a starbase with the propulsion bonuses and the enemy propulsion penalties makes even engineless vessels more than adequate to defend a region of space from any sort of threat without having to stack them right on top of the starbase.
Since everybody in the universe was at friendly or better I didn't think my lack of military was going to be a problem...
Just out of interest my military doctrine espouses the construction of tiny and small ships without engines. These are Light Fighters and Heavy Fighters respectively. They are for system/starbase defence, are cheap to produce, maintain, and gain the biggest benefit from starbase module stacking.
Medium ships are constructed around a twin engine extremely fast but lightly armed warship design. This is the Strike Cruiser class and they have two of the latest engines as well as a blend of offensive and defensive options (all my ships carry defences - I play the good alignment)
Their primary role is harassment as well as taking out targets of opportunity eg stripping planetary defences, unguarded troop transports, starbases, damaged or lone enemy warships etc. They also excel in escort duties, freighter protection, emergency fleet intercepts and just about any general combat related task against equivalent tonnage or lower. In a fleet of 4-5 they are very potent but typically I run them in task forces of 3.
Due to their lighter offensive armament they can be temporarily assigned to my main order of battle (large and huge, Battleship and Dreadnought respectively) without drawing enemy fire and serve as a force multiplier. (especially useful when battles occur within military starbase radii)
Battleships and Dreadnoughts only use a single engine opting to go weapons and defence heavy. They can afford to do this since I have roving task forces of Strike Cruisers handling tasks that require rapid deployment - late game Strike Cruisers start hitting the 12 - 15 parsec per week mark) Not to mention the fact that engines for the larger classes of ships are huge slices of the available space.
Anyways my point after all that, aside from geeking out over my defensive fleet design, is that there are plenty of ways of defending starbases and utilising starbases other than just making a super stack. If anybodies interested I can go into more detail about my fleet design (yes that was just the Cliffs notes - can you tell im excited about the new possibilities in TA?)
Also on the note about starbase values - it automatically updates when your ships are under the area of effect. To test this build a ship with a railgun then put it under the radius of a starbase with a laser equilizer. The ship should now have a beam weapons rating - it may take beginning the turn within the radius to show up.
The AI should react to the updated stats - I have seen the AI flee from some of my 'puny' fighters presumably because it saw they had about 20 modules worth of upgrades backing them up

On happiness. Typically I run my colonies on 76% or better to ensure the 1.25 population growth bonus (I use the Populist government choice to help with this) This can get a bit tricky once you pass the 20 billion mark.
On average colonies I wont exceede 20 billion. On cash/trade hub planets I go up to 30 billion but no further. 30 billion is already really pushing the limits on happiness and only really possible on planets with the political capital or secret police centre and the like.
Since I do this on 50-60% percent or more tax levels without happiness becoming too much of an issue it sounds to me like you have very large populations. There seems to be a really hard ceiling on population that no number of virtual reality centres can deal with.
If that isnt the problem then I'd like to hear more so we can figure out a way to help you out with it