Since the idea of a 10/22 with a Butler Creek folder seems to appeal to you, might I suggest using the nifty little Compact version instead of a standard carbine? All of the design's inherent virtues in a smaller, lighter package plus it comes equipped with a set of easily adjustable Williams FO sights.
It's an idea I've been toying with myself for a while. I've owned at least one example from all of the several different makers of the AR7 design. IMHO, a brilliant concept and design, but all-too-often dismally executed due to changes to the original component materials specs to cut costs and notoriously wretched QC.
I really like my Springfield M6 for its very compact design, ruggedness, mechanical simplicity and potential for versatility. Unfortunately, they have been out of production for some time and nice examples have become fairly pricey. Still, for a "just in case" firearm to be stashed with other emergency gear in the trunk or tucked into your backpack while camping or trail walking it offers an awfully lot of valuable features for what little space it takes up.
Personally, I took an excellent condition Norinco-made Browning .22 Auto copy that I picked up very cheaply and used it as a base to try out some ideas.
I had the receiver drilled and tapped for a Lyman 66 receiver sight, replaced the rather crude factory open rear with a Marble's folder, replaced the front with a Marbles FO bead and added attachments for QD swivels and a carry strap. I also bought a padded cordura case for it from Galati.
All parts, labor and accessories included, I still have a bit less than $275 total in the project. It's working out extremely nicely for me so far. About 5 lbs., 9 oz. fully loaded with the strap, a tad over 21" long taken down and cased, excellent functional reliability and (even with my 63 year-old, bifocal-clad eyes) delivers 7/8" five shot groups at 50 yds from the bench with CCI Mini Mags or WW/Super X Power Points when I do my part well.