D'Addario used to make super long .135s, I had a tapered one, excellent string, shortish taper and flexible. But 2 years ago they discontinued their super long single strings. At that time I emailed
http://www.stringsdirect.co.uk to order some single .145s, they said there was some stock left over at D'Addario UK.
So perhaps email them and ask if D'Addario UK have some super-long .135s lying around? I recommend the tapered version, especially for the 45 degree break angle over the saddle of a BTB (I own a BTB).
The latest D'Addario long scale strings are now 36&1/4" winding length so
might just be long enough for a BTB.