Just to add, for any other strawberry novices trying this out there, the little pots of new strawberries are taking root now and the vines are sort of dying away by themselves, as the new plants root. Strawberries really know what they're doing! 
I'll cut them in a few weeks once I'm sure everything has strong roots.
Thanks to everyone for their suggestion and advice on this!

I'll cut them in a few weeks once I'm sure everything has strong roots.
Thanks to everyone for their suggestion and advice on this!
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