I treated myself to a 4-speed sliding hook flyer for my Traddies and Traveller, which comes with a much bigger bobbin, so I use that bobbin for plying - it takes more than 2 singles from the standard bobbin, in fact I can almost get 3 singles on when I do my 3-ply. (3-ply doesn't take up one-and-a-half times as much space as 2-ply, just a little more.)
I would cut it, wind it off onto the niddy noddy, then ply the second halves. You either have to join while plying or while knitting, and I don't mind splicing yarn while knitting. (But then I have a large bobbin to use in the first place.
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Have you been told about washing the wool to set the twist? I usually let it sit on the niddy noddy for 24 hours, but that's not essential, then (having tied it in a few places so the strands remain ordered through the washing process), wash, snap, beat if required, dry, then wind into a ball for knitting.
Shout if you need descriptions of any of those stages!