Let's give this a shot and see what happens...
 

First:

Retrofit Phasers. Man, I love the look and sound of these bad boys. Not to mention they scale with your level. So, only thing we are missing is Retrofit Dual Beam Phaser Arrays. Would honestly complete the set and I am sure I am not the only one that has requested/thought about this.

Second:

Refit K't'inga. One of my all time favorite Klingon Ships. One I do not ever want to be forced out of and would like to see it go to Max Tier. How can we make this work? First, at higher Tiers it will still be a Cruiser. So let's double or even triple it's size, but keep the same body style, This way it will make sense as to why the Turn rate is suddenly so low, perhaps match that of a Star Cruiser. Give it some interesting perk, add whatever slots the Devs feel it will need to make it on Par with it's counterparts and adjust Hull Strength to match that of a Tanker type ship. Presto.

Third:

Can we maybe change the fact that Science Team cancels out Engineering Team? This makes zero sense. So when my Engineering Team are hard at work repairing the Hull, my Science Team has to sit on their butts watching them work? What is this, the local Water Company?

I like this idea regarding the phasers. Even better would be the ability to craft them up to very rare procs.

I agree with the sci/eng team problem. What is the logic behind one precluding the other?

maybe the engineering controls also doubles as the sciense controls :P and they only have a few set of consoles that do that job .... defys logic and what we've seen in the show but still :P

I always explained it to myself that the eng/sci teams had to take turns lining up to use the transporter room, since the various Team abilities fall under Crew systems and it even makes the transporter sound when you use one. It's like the science team is beaming to the area on your ally's/your own ship that's in trouble.

Of course, my explanation doesn't cover how the problem's fixed as soon as they beam over, or that they can beam through shields during battle, but after all, it's just a game. :)

Union rules stipulate only one crew is allowed to work at a time. Violation of that rule can result in severe penalties to the ship owner.

or

Your Engineering Team is your Science Team. They change uniforms between jobs.

They don't even change uniforms. They're just crew waiting around to be told what to do. Sometimes the chief engineer tells them what to do and other times the head of sciences tells that what to do. :)

And then they die and come right back to life.

Oh, the life of a Starfleet crewman. :D

I really like the idea of Retrofit Dual Beams, and the refit K'tinga.

As for the sci/eng/tac team global cooldowns, it's more of a transporter cooldown than anything. And I believe it's in place for gameplay's sake.

I have never asked for the cool downs to change in the past, because the abilities used to come with a hull/shield resistance. Now that all they do is a simple heal with no extra benefits, I see no reason for the continued cool downs.

This is incorrect, they are not just simple heals, but powerful ability counters.

A quick fight with the Breen highlights this. If you use your science team to counter a Breen cruisers SubNuke, you wont have ET available to counter their Target Subsystem attack they often use as a follow up.