So I completed the Covenant quest line and decided to kill everyone since I had Cait with me. However, you can imagine my dismay when I realized how truley bugged this settlement is. Is there anything we can do here to bypass the bugs or somehow claim full ownership?

I just scrap everything I could, works on most of the loot, there are bits that cannot be scrapped and thus do not transfer ownership to you.

You on PC? If you use console commands you can click on anything and hit "setownership" in order to make it free to take.

This, though scrapping them is much faster. I actually left most of them as "steal" to avoid the hassle of having to set ownership on everything but still maintain their pretty arrangements by not scrapping them.

I also used the 'markfordelete' command to get rid of stuff like the original turrets and the bunk beds so that I could replace them with stuff I wanted.

Some of the crops aren't functional, either. Since just Cait and I live there with a gate guard, artilleryman, and a servant/farmer, I didn't bother messing with them. I just planted a few mutfruit trees to feed the staff and left it alone.

Are there any repercussions for stealing items in Covenant after killing everyone but before setting up the Radio Beacon to invite new settlers in? According to the wiki, you can go into workshop mode, store the items, and then take them out of the workshop without problems though.

Another problem with Covenant is that the original turrets won't count towards the defense rating of the settlement so you need to use the markfordelete command (if on PC) to really get rid of them if you want to build your own turrets where the old turrets were. If you just destroy the old turrets then their remains stay keeping you from building over them, and you do have to get rid of the old turrets since they'll fire on the new ones you build.

I am on the PS4, but I bought the PC version for my 2nd play through. I created a beacon to test assigning a settler to a bed and it worked. That is good enough, I can build upward and just create what I need. It was rather amusing killing the town, I am level 42 - they were hitting me with pebbles, hardest part was dragging the bodies out. My wife woke up at 1AM and came to the loft, asking what I was doing - "I killed everyone in this town and now I am dragging their bodies to the river..."