I've not had any problems with reagents, including R-0871, I purchased in one season and carried over to the next. I keep them inside away from light and heat and I never keep them more than 2 seasons.

I think you would be fine getting the R-0871 now and using it next season. You could get it directly from Taylor if you want to make sure it's from a fresh batch.

Concerning your original question, I have a few kits that I used (purchased separately) and have thought of getting a small tackle box to keep everything in. I would think it would work great for that.