Building constructors was a mistake, but not a fatal one. Dread Lords find starbases irresistably fun to destroy (keep this in mind in other scenarios where you see them, such as in the DA campaign). Building freighters was a good move, though try to arrange the routes to be as far as possible from the DL (right hand corner to the Altarians or Iconians, for example).
This scenario is incredibly annoying and tedious, but you're doing fine so far. You may well lose the ex-Drath worlds from time to time, but that's OK. In my game the main fighting was over the Cordelia worlds in the center. You already know what to do, so keep doing it. Play "dodge the Dread Lords" every single turn with all your sensor platforms and fast fighters, pop troop transports whenever you can, and tech up. IIRC fleets of medium frigates can kill small DL warships at great cost, and once you get large hulls you can tie rule those DL ships (Escorts and Fighters) and take down frigates with fleets. The DL tend to be bad about defending their conquests, so fast transports should be able to take planets when opportunity presents itself. Eventually you'll steal a good tech like Black Hole Eruptor rather than useless junk like Space Mining or Advanced Toxic Colonization. Once you have the tech to tie rule DL frigates, game over!
Other tricks you may well already know - use spies to try to keep a lid on DL worlds you can see. My sensor drones could only uncover one of the Gladstone DL homeworlds, but it was full of spies by midgame. Do the hive mind tech trading thing with your teamates, sometimes they'll research something useful for you, and at least you can keep them from duplicating stuff you've already done. In my game, the Altarians, Arceans, and Torians took care of the gun research tech sequence, while the Iconians and I worked on missiles. Makes it a bit harder for the DL AI to refit their ships with on-type defenses.
The other way to go would be to find the cheat code to "win" the mission and move on to the next. Apocalypse is by far the most irritating campaign mission...