Micromanaging large fleets?

It may be that your just not building enough of them, the whole point of ability ships is that they can't take hits that well. Thats why they have less fleet points and are normally cheaper (sorta) then the real heavy hitters.

Maybe you should try having them 'sit' by your capitals (set the attack radious to just range not the whole gravity well) give them the extra protection of the fire power and keep them away from the major front line

In broad terms you can classify the ships into support and combat.

The job of combat ships are simple, do as much damage and blow as much as you can up before they die; when you decide which ship type you build you need to take the following into account; does my ship counter the enemy fleet, does the enemy fleet counter this ship, I researched some upgrades for another ship type would I be better off building those instead, are these ships viable in the long run, if I build these what will he build, will this type of ship work well in cohesion with my allies fleet, how quickly can I build these, if I build these am I making it so my fleet has some high dps/low hp ships (for the enemy to kill first) and some low dps/high hp ships. That might be a little overboard especially for single player but they are all things to consider.

Support ships on the other hand have 3 roles keep your ships alive, increase the efficiency of your ships and decrease the abilities of the enemy ships, most support ships fulfill 2 of those roles, some are better late game and some are better early game some aren't worth building in 99.9% of the games, I'm not going to tell you which support ships to build and which ones are worthless you can experiment and figure out which ones you like.

A lot of things depend on fleet composition, but support cruisers are incredibly powerful, and the Stilakus Subverter, Hoshiko Robotics Cruiser, and Iconus Guardian are in particular quite deadly.  These can disrupt the enemy's ability to attack or retreat and leave them sitting ducks to your forces.  Casualties are normal and you should expect expensive support cruisers to die first, but their abilities are almost always worthwhile (the Domina Subjugator is the only real exception to that rule).  Losing Overseers is nasty, but if they are keeping capital ships alive that is what really matters.

Generally as fleets get very large, strike craft start to become exceedingly dominant units.  The light carriers shouldn't be positioned with your main fleet unless you're Advent with a Rapture Battlecruiser.  For everyone else, light cruisers should be positioned far from the battle and ready to jump out if dangerous enemies get too close.  Large forces of strike craft are absolutely devastating, especially to heavy cruisers.

How exactly do I keep my carrier cruisers together though?  Is individually shift-clicking them the only way?

If you only give your units attack orders once in a hostile gravity well, your carriers should stay put at the edge of the gravity well as they don't have weapons to attack with. Or just let your combat unit move to autoattack a bit and they should separate themselves quite nicely. If you want more precise control I manually edit my [diplomacy.]user.settings file so the stack size is 999, effectively allowing me to give orders to all of 1 unit type in a gravity well with two clicks using the Empire Tree.

Use alt (then click on a ship) to select all of a type in a grav well, you can use this in conjunction with shift to select all of a type then deselect some or select all of one type then add all of another type to your selection.

Shift: Que orders, click/drag add/removes from selection, used for some commands like scuttle, change black market/feed/pirate bounty amount

Alt: View tactical information, change click select to all of a group

How about Overseers?  Is it best to just let them roam free within the main fleet, and just hope they repair anything that needs to be repaired during a fight?  I've seen my capital ships dying right in front of them previously, where I had to find the closest overseers in the huge crowd of units, so I could manually heal him. Is there a way I can order all my overseers to simultaneously use their heal on a single target, now that I know how to select all of them?  Or do I have to just cycle through each and every one, and individually execute the heal on each of them?

On another note, I recently discovered that overseers can only heal units that they are facing, which seems like a huge disadvantage to me since the turn rate is very slow.  I don't know if robo/command cruisers are the same.

What I do is put overseers on hold position and turn auto attack off and make sure they are in range of what will need healed.

If you have them all selected, you can just click the ability button and select the ship to be healed and I think they will all attempt to heal.

In my experience, I've always found it helpful to set your utility ships to non attack so they stay back a bit from the fray. This won't prevent them from using abilities on allies or enemies but keeps them from running point blank to the enemy fleet.

I've started doing as you've all suggested by using alt-select, and setting auto-attack off on my support cruisers and things are working out a lot better now.  What's sad is that overseers are still taking a long time to heal their targets because sometimes they need to fully turn around to heal, unlike robotic cruiser.  For a capital ship though they still get the job done because it can stay alive long enough to give them time to heal, but with smaller ships scattered all around them they can't rescue nearly as often as robotic cruisers can.

Yes the Vasari are much better at healing larger targets like capital ships and starbases while TEC is better at healing a larger number of ships. (for healing a large number of damaged ships Vasari players are better off using repair cloud then overseers)