I can't believe it took me this long to figure it out. Any weapon you want your Federation or Romulan starship to have, but it belongs to someone else? Here's how to get it without editing ship defaults and rendering that ship invalid in the latest patch.
As always, BACK UP YOUR FILES BEFORE YOU EDIT.
Go to your weaponitems.txt in the common settings folder of your assets directory. Under each weapon there will be a line that looks like this:
Race = "F"
This line indicates that the particular weapon belongs to the Federation. However, if you'll scroll all the way down to the antimatter minelayer, youll see the race line like this:
Race = "BFKR"
That's right, a weapon can belong to multiple races. So scroll around and find that weapon you want to add to another race. Say the weapon is Klingon and we want the Romulans to have it. Find the race line and Just add a capital R to it like this:
Original
Race = "K"
Edited
Race = "KR"
Save the file. You'll find the weapon available for refit in both the Romulan and Klingon refit screens now. It's pretty obvious what letters represent what races, so it's really easy to do.
Good luck.