I can't tell you specifically which has contracts still, but I doubt any of them do.
There may not be quite the shortage of qualified pilots here in AK that there are elsewhere, but it is definitely felt.
I would contact them directly, if you are interested. Apply.
About how quickly you can go from RS of the 208 to LS of the 207; It would depend greatly on your flight time and how hard you are willing to work.
Alaskan based co. are usually very interested in how hard you are willing to work...not just on how good your flying skills are. They like guys that are willing to throw bags and help on the ramp when they aren't flying. And be willing to learn....even from a crusty old fart who doesn't have any jet type ratings.
That "don't like to get your hands dirty" works for 121 ops., not for 135 - at least not in AK.
cRB