Tie it together with two (2) bits of 5mm accessory cord (right size for general camp use, bear bags, BDSM games at home, etc.) or light weight climbing nylon tubing.. Light weight tubular webbing (like you would use for climbing, esp. winter climbing, maybe 5/8") can also be sewn to anything/anyone with dental floss and the awl of a Swiss Army knife, and backed up with an attractive wrap of duct tape. You can also just poke holes w/ awl and use cable ties to attach straps. I used to carry some seam seal in my repair kit (haven't looked in their for a while).
You will always find a need for both the light webbing (although I do have friends who hate me tying off ice screws with it) and 5mm accessory cord (not the 550 cord, not the 5.5 mm kevlar/spectra cord designed for string hexes) all the time, so throw out the boot laces (either will work just fine). While the webbing will hold leader falls (I tend to reserve it for snow), don't use the 5 mm for climbing, other than Prusiks (both the webbing and cord will work for this, although you should use a KKlemheist knot, Prusiks are for chumps).
I like the split ring idea a lot, but would use a pair of aluminum rappel rings (which I likely have anyway) or some steel D rings w/ sufficient strength to double as rap ring. These should not be confused with split peas, which are for eating Plastic abseiling rings*, while light, should be avoided at all costs.*
I like Peteris' idea of carrying webbing and buckles, but I would sew these to the outside of the pack and use it to carry my rope, shovel, jacket (always nice to have handy), camera, or other things where you can easily stuff them in the pack/under the lid of the pack if needed, and are light weight so they don't rip things out.
Use mono-filament fishing line (but be careful with knots--a dab of seam sealer or blue on the end of the not is not a bad idea) at home in a running slip stitch. Cut the knot and pull the thread and the whole thing just pulls apart. Dental floss is essential to getting still-wooden freeze-dried beef out of your teeth (your mates will thank you), and is a very strong. Waxed is harder to pull through multiple layers, but sort of water resistant. The Goretex stuff I use at home seems strong, but is slippery as an eel, so use fisherman knots.
If you have a lot of duct tape just tape a little bit around the broken strap area, and have a friend wind a half-dozen turns of it around you and your back. Not comfortable, not Eco-friendly, not attractive, but if you go w/o a shirt you can probably aim the tape to skip some body waxing/shaving you have been putting off for a while.
Page 1, rule 6: "Scramble, be flexible". (Philmont Ranger's Handbook)
Having shit go wrong is how you get experience, so if you want to get more experience try to carry a bit more repair stuff, first aid stuff, fire making stuff, etc. when starting out so you can try different things out. Then if things are not breaking down enough to give you experience as fast as you want, start drinking. Nothing makes catastrophe occur quicker in the outdoors than a few too many. So if you are just starting out, go out of your way to make a lot of (safely protected and/or minor) mistakes just to get experience fixing/recovery.
*There is no such product and I suggest never making one. While there are polymers which can probably handle the load, who wants some punter putting a polystyrene loop of plastic chain up?
The only exception is for the Australians who jumped in front of me on a climb at Red Rocks in NV only to get stuck w/ loudmouth leader who couldn't lead a 5.7 without bolts, didn't know how to self-rescue, and who took a dump on the climb and didn't clean up).