Welcome to The Forum, Charlie, and congratulations on the 266RKS! I have one, too - a 2013 I purchased new in January. Don't you just love the layout, the countertop space, the storage space, and the huge storage tank capacities? I had mine out for its maiden trip about 3 weeks ago, and it performed flawlessly. Hope you're as happy with yours as I am with mine.
What are you pulling it with? Be sure to post some pictures when you get a chance.
As for mounting the levels: I know what you mean about drilling & screwing into that new fiberglass, but I think short screws are your best bet. Just don't drill/screw into your propane tanks! (LOL) And put a good dab of caulk into the screw holes before you insert the screws. Can't remember who posted it, but there's a thread on the forum about how hot these brown caps get. I'd be afraid the heat might soften the glue on double-sided tape, and you might loose your levels. I'd also be afraid that pop rivets might crack the fiberglass. JMoony's suggestion of Liquid Nails is good, too.
Best of luck with your Eagle! Hope to see you 'round the campfire!