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If drops/hoods don't work cos of your lower back, I suspect cos internetbikefit too much reach/drop. (f.e. a 49*53 is common but I need a 50 or 51 square...)
If you don't get a frame with a stupid* carbon steerer you can not cut it down much and that will give you height. Perhaps you can get away with a 58 square and raise the quill stem/one with an uncut steerer if it must not be modern?
F.e.: http://www.ebay.co.uk/itm/Holdsworth-Replica-Fixie-Bicycle-Frame-/131748880116?hash=item1eacd85ef4:g:ZLMAAOSwoBtW4e6Z and get a crabon fork for it and leave steerer high?
Or http://www.ebay.co.uk/itm/Vintage-Ellis-Briggs-Track-Frame-And-Forks-Leroica-Reynolds-531-/231784908003?hash=item35f77504e3:g:hKwAAOSwk1JWcDo1 and a high quill. (Nitto does them, ppl do complain about quill stiffness though)
Most frames seem to be longer than higher...I've seen customs though in the classifieds here, and I believe Ueno had a short/high frame so worth an ask too. Good luck :)
*stupid yes as you can't use more than 3 cm spacers.
Tried drops and hoods, love all the hand positions but my lower back couldn't take it over longer distances. 30+ miles in a day we are talking here.
Not a fan of the look of crostop levers on drops :/
Any suggestions for tall/short frameset? 62/58 would be good, 60x60 is what I'm currently riding