I had the same thing happen to me...
I just finished a game, basically winning on influence, as the Terrans. The DL showed up late game, and within a few turns had a ship on their homeworld with a ?? for missile attack. When the ship launched, it had a 850 attack, with no defenses and 117HP. They started after all the other races first, and made peace with them, which I though was odd also, until they got to me. I tried to speak to them, when the message came up that said that "the galaxy was two small for the two of us," and the game responded that a meeting would be setup in a few week, stating that this would happen because of being a supper diplomat.
Regardless to say, the meeting never happened, and with this one ship, they started taking out all my infrastructure, trade routes, starbases, ships, etc. I was playing on a small galaxy, so moving around to all the infrastructure elements, was quite easy for them.
It was later in the game so I built what I thought would be a ship that would destroy this ship, and finish them off for good. I build a large hull, attack 125 beam and with cash I had, bought three of them, launched two and put them in a fleet. Lets just say that things did not go as planned. I lost both ships, but the DL ship was down to 1 HP. So I launch the final ship, and attacked. What happened floored me. Not only did I not destroy the DL ship, but it destroyed my ship, and was completely back to full HP, assume that the XP it received by destroying my three ships, was enough for it to level. At this point I tried reloading the saved game a half dozen times using different tactics using these three ships, against the one DL ship, and every time I failed, so I just continued the game from that point forward.
Needless to say, since the DLs had destroyed all of the other races fleets before getting to me, and the fact that I could not even touch the DLs largest ship, I took to invading the rest of the races as fast as possible, it was a race to the finish, the DLs were taking out my infrastructure, while I took out the other races, and the game was own on influence, with the DLs still running wild.
This was my first game of DA, after playing DL, and I have to admit, the twist in late game of the DLs showing up made it very exciting and actually made me continue playing even after I though I was over the "hump".
That being said, I am torn between not wanting to change a thing, because it forced a change in stratagy late in the game, vs wanting to be able to stop the DLs, using the military that was, IMO, far superior, to anything else in the galaxy, save the DLs super ship.
That sounds very similar to stuff I've experienced just in the past week or so. In my last game of DL before purchasing DA, I had a Terran frigate get its hit points re-upped like you describe above. I had spend my whole wad in the area to whittle it down to what should have been 1 HP (fodder for my one remaining fleet), but after the final battle the frigate got an experience boost and a full recharge. Aaargh! I submitted a bug report on that one and Jessie has been working it. Unfortunately I had no save game to submit to reproduce it.
As for the DL in DA, your description sounds very much like what happened in my game, except I am only just barely into mid-game and my ships are nowhere near the power of yours. The DL can swat my best ships away like a bug. This doesn't seem to be in the best interest of good gameplay to me. I didn't mind having a pirate infestation which took out all the infrastructure just prior to the DL showing up, as the pirates are not expansionist. Once you kill their ships they're gone. But the DL takes worlds and operates like an ultra-powerful empire and is simply suppressing all activity of the AIs they were at war with. My last strategy was similar to yours in that, since the DL were taking out all the Yor defenders, I found I could rush build spore ships and grab chunks of their territory very easily. Problem is, when I did that the DL eventually just took all of those new planets away from me as easily as if they were clubbing baby seals. If I can't find a way to stay at peace with them while I build up, this particular game looks completely hopeless.