Many people talk of having small hands & having trouble with fretting even standard chords...but in all honesty, more often than not, it has more to do with their hands just not being used to stretching and contorting the way that they need to to form chords and fret notes cleanly.
I would just start with the absolute basics, open chords, basic pentatonic scales, etc.....and just keep at it. Even with prior experience on other instruments, it really does take time to get the hands into guitar "playing" condition. As far as callouses go...I play pretty much every day and have for years & I really don't have heavy callouses at all. I've known players that play half as much as I do & they literally have to file their callouses down.....I've never had that, so it will vary from player to player. There is no set time to give anyone.
As far as guitars go....A Martin Backpacker is made more for travel & convenience, rather than a big, clear, full bodied acoustic tone...so don't judge yourself too harshly on that alone. If you are serious about playing and really have serious trouble reaching notes on a "standard" scale guitar...you might try checking into 3/4 scale models or something. As a general rule, a smaller bodied guitar will almost always have a "smaller" tone than it's jumbo bodied, full scale counterparts (acoustically speaking at least)....but there are well made, serious 3/4 scale instruments out there to be found....you just might have to do some intensive searching to find the one for you. Also, since the "Fit" of the guitar will be of utmost importance to you, I would focus on trying them out in person, as opposed to ordering something blindly online.
BTW, ont the subject of 3/4 scale instruments...I tried one of these out at a local store...and they are actually pretty nice playing, well designed guitars. (You might not be a metalhead...LOL...but this is just an example of what's out there)
Hope that helps a bit!
Don
