Hello Joseph, 

You have asked an interesting question.  In 3/1 twill there is a float
over three threads which may be a bit long for bobbin lace.  However,
2/2 twill has a float of only two threads which I think might hold
together better. 

I decided to try and figure out how I would make 2/2 twill using pairs
of bobbins and just slightly modifying the plain cloth technique.  The
explanation required some pictures so I decided to post it on my blog. 
I am still working on the description and, in particular, I now need to
go and make some samples.  However, if you want to see an early draft of
my idea, here it is: 
https://tesselace.com/2018/12/20/2-2-twill-with-bobbins/ 

Thank you for the nice puzzle. 

Kind regards, 
Veronika Irvine

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