I believe I figured out a solution.
Using some old copper I had, I crafted a piece to go up from one of the clips, and into the hole on the board. This SHOULD do the trick.
Spoke: Before I power this up, is there an issue with this piece being grounded?
I like it! What is that plastic piece that secures the bottom of the clip? I saw those on my housing but didn't investigate.
The thin clip won't give much up and down stability but I think the PCB is pretty tight in the housing so there should be little up/down movement.
No worries about shorting out at the hole locations. As long as nothing touches the LED leads you'll be ok. Let me know how these look when you power them.