Cherryrock --- Have you tried doing it on sewing machine bobbin winder?  With a little care not to tangle it just might be possible.  But, the expense of all those bobbins might be a bit costly.

I was in same fix.  Or very  similar.  Filled 5 tightly packed thread boxes crammed full.  Had to hand wind all with that DMC hand winder.  It took a few days doing practically nothing else.  But, got the job done.  Glad I took the time.  It sure made stitching a lot more enjoyable.  No more searching & comming up empty handed looking for a specific color #.

Once you set your mind to doing it & sticking to it till the job is finished you'll be glad you did it , too. ----- Citrine1