Thanks for all the replies. Update - I just ended up cutting back some backing to make room for it. When I am done Euro Nymphing I run the whole 40 foot leader out of the guide and wrap it on this 6 inch rigging foam thing i got on amazon, then my floating line is ready to be used. When I want to switch back, just add the mono rig back to the floating line.
For me, I like to switch between euro nymphing and dry fly fishing throughout the day. This system allows me to do it. I know its possible to dry fly fish with a mono rig but I dont really care for it that way. I also know its possible to nymph with a floating line but same thing i just dont like the drag that floating line creates on the water. I guess I am just weird but that is what is cool about fly fishing you can come up with own system there is no right or wrong way.
I also listed to Troutbitten and they have some great info. George Daniel had some great insights on the Orvis podcast too.
But thanks to all on here too, really helps a beginner out with the suggestions.