I got to Tier 5 in the Romulan Reputation system last night and the Omega Reputation tonight. I'm trying to decide what, if any, of the sets or new gear I should get. I'm an engineer in a Defiant-R. I don't PvP, I do STFs, and occasionally fleet missions. My fleet is at tier 3.

Here's the setup I've got now-

3 Antiproton Dual Heavy Cannon Mk XI [CrtD]x2 [Dmg] (old STF weapons) & Omega Plasma Torpedo Launcher
2 Antiproton Turrets MkXI [CrtH]x2 (old STF weapons) & Cutting Beam
MACO Mk XII space set
3 Neutronium Alloy Mk XI
2 Field Generator Mk XI
3 Antiproton Regulator Mk XII & Assimilated Module

BOFF powers are
Cmdr Tac- TT1, CRF1, TS3, CSV3
LtCmdr Tac- THY1, TS2, CSV2
Ens Tac- TT1
Lt Eng- EPtS1, EPtS2
Lt Sci - HE1, PH2

Active DOFFs are
Purple Space Warfare Specialtist vs Borg
Green Energy Warfare Officer- reduce cannon special attacks
2 Purple Projectile Weapons Officers
Technician- reduce BOFF cooldown.

Should I replace any of this gear with some of the new stuff or switch anything else around?

You should replace the Technician. It only works if you use the ability Auxiliary to Battery. A shield distribution officer would be a good choice.

Your weapons look all right for taking on the Borg, but like scurry said, take off the technician and add the Shield Disribution officer.

Personally, I'd opt for a Projectile Weapons officer to reduce cooldown on the Omega Plasma Torpedo Launcher

I've got two Projectile Weapons Officers now. Would a third be that much better over the Shield Distribution Officer? Does it impact the recharge time for the Omega Plasma Torpedo Launcher? I know they worked awesome when I was using photon torpedoes, but I wasn't sure they would work on the Omega Plasma.

tbh, I'd use only one.