I've put drop bars on a similar bike (a Jamis Dragon Pro) and I'm about the same height as you, 6'3" with 34.5" inseam.

I needed a very short stem with some rise to it, and the Reach was still pretty long. Ironically it has a pretty short reach with flat handlebars.

Normally I would say the Large Kona is too small for you (I've also owned a Large 2011 Kona Unit) but with drop bars it may be OK.

 

Normally I would say the Large Kona is too small for you (I've also owned a Large 2011 Kona Unit) but with drop bars it may be OK.

Was the Unit 2011 Large too small for you?

 

Yeah, it was a 20", I'm on 21 and 22" now. But I still rode it for 2 years till it broke.

 

find a bike that is designed to fit you with a drop bar like a road, CX or touring bike. note the effective top tube length and stack. compare that to the ETT and stack on the Unit you're looking at. can you make up the difference with an unconventional stem, or is the handlebar going to be too far away with most options?

to visualize it, try plugging in the number for a road bike that fits you and compare it to the geo on the Unit:
Stack and reach calculator