Well mister Drinkwater there is only one brand I would recommend and that is http://www.circlekstrings.com/store/
I would go with something like .150 or .158
I've been tuning to F#0 and lower for 14 years now and have been disappointed by the biggest gauge of a lot of brands.
Rotosound/Warwick .175 may be long enough (a little big though) or you could custom odder LaBella or http://octave4plus.com/
S.I.T./Conklin .165 will not work on a 36" scale (35.25" speaking length) can not verify the .150 but for that price Circle K looks pretty reasonable.
If you do find something you like better than Circle K let me know 'cause they've been getting all my "string money" for about 3 years now.