I think you have the right approach by being vigilant and knowing that as you do not have symptoms it can be hard to know how you're faring.
Personally I'd stay clear of oats and anything with barley in it, even if it's labelled as GF. (You probably already understand that occasionally products have barley highlighted even if they're under the 20ppm GF limit. Barley is an allergen and the smallest quantity can be toxic for some people who do not have CD, which makes the labelling tricky to understand for coeliacs.)
So to start with I wouldn't eat malt vinegar, oats, yeast extract (apart from one brand, which does not derive from brewer's yeast) pickles containing malt vinegar, cereals etc etc.
Re contamination form crumbs.....we all do the best we can with this. I'd say to make sure you never use the same toaster/butter/jam etc as a gluten eater. Of course there will be times when you might accidentally ingest gluten - it's everywhere! - but the thing to do is to take proper steps to make sure you're safe and then relax and enjoy life.
If you get a good routine going you will soon eat safely and know you're on the end to recovery. Don't sweat the minutiae yet - there's enough to be grappling with in the beginning rather than worrying about the stuff you can't control!
Everyone makes the occasional mistake and the effects, if felt, don't last too long.
Best of luck...
BTW, as you're an asymptomatic coeliac, I'd make sure you have a follow-up blood test in 6 months or so to check how you're doing...