Is it necessarily bad to have a short stem, though? One of my bikes started life as my main mountain bike back in the '80s and has been revived as a commuter, loaded tourer and now a singlespeed that lives under the stairs at work for runs to the coffee place. It's had (quill) stems from 150mm down to 70, as I moved the bars around for one use or another. There were differences as they changed, but none of them presented a problem. It takes about 10 seconds to get used to the new feel.
For the OP, I'd be inclined to go with the larger frame. I'm 6'4", which is a little larger than most bike shops can fit with what they have on hand or can order easily. I rode 62cm frames for about 20 years because that's what they had in stock ("We'll put on a longer seatpost for you--it'll be fine"). I rode tens of thousands of miles that way, and thought I was as comfortable as you could get on a bike. When I bought my midlife crisis Atlantis, Rivendell's sizing chart put me on a 65. I was dubious but followed their advice, and it's made a huge difference. Instantly, I could stay on the bike 50 percent longer without being uncomfortable.