I think I'm making this too hard, so figured I'd just ask the experts...

I'll be connecting in FRA on two separate itineraries and have a question about carryons/checked bags. I usually carry on one small duffle that fits under the seat and one backpack that fits overhead on my flights. The rest of my flights on this trip are business or first and it doesn't appear to be an issue on those flights. However...
I'll be on LH from LJU (Slovenia) to FRA in economy and reading the policies it appears I can have only one 18lb bag carryon. (Does LH strictly enforce weight?)
There doesn't appear to be a way to purchase an additional carry-on allowance. In FRA, I'm flying on a different itinerary to JFK so I won't be able to check a bag through.

I'm assuming since I'll be traveling from a Schengen country to a non-Schengen country, before then going through passport control to exit to the US, that picking up a bag isn't an issue? That is I didn't have to pick up a checked bag that I couldn't otherwise save time if I had no checked bag (recognizing I may have to wait for the bag to arrive, but I couldn't have headed directly to the next gate). In other words, I essentially enter Germany anyway then it's like I'm just departing for the US as if I arrived at FRA to start my trip?

(This may be a moot point as I may take an earlier flight in and then head to an airport hotel anyway to take a nap and shower, but just trying to evaluate options here. I'm pretty certain I can leave the airport for a brief time while in transit to head to a hotel.)