That's cutting it too close, probably both ways. I know a few others mentioned it, but the San Jose Airport is not in San Jose, it's in Alajuela (which is west of San Jose). Some people have taxied it to the ferry on arrival and then caught the bus from Paquera to Montezuma, look around the forums for details.
My experience is the directo from Montezuma is when they put your luggage under the bus (usually in Cobano) asks "Aeropuerto?" and marks the luggage and then knows to stop.
I'd consider the Airport very safe to hang out. I've done the 2am flights but (in my experience) they don't even open the counter until a few hours before (Spirit two times specifically; but I've had others not check me in extra early during the day even when the counter was open).
The check-in area is BORING and if you can't check in way early you're trapped there. If you bring anything that needs to be plugged in (for entertainment) bring an extension cord with a splitter, the plugs are in bad spots and if someone else is using the plug, the splitter will get them to share since they can stay plugged in(!).
Montezuma Expeditions does some shuttle rides with a Alajuela hotel combo (including taxi) to or from the Airport, that would work for you either way, but probably more useful on the way in. I've used them MANY times.
Personally, I usually go back the day before (on a late bus/shuttle) and stay in Alajuela (at "Casa Tago" hotel/B&B 5-10 min from airport, they'll hold your luggage after check out until you go to airport). If you're spending most of the time in Montezuma, I think it's worth checking out San Jose or Alajuela for an afternoon. Alajuela has a little downtown area but it's a metropolis compared to Montezuma. Or I'd head over to San Jose for part of the day (there is a cheap directo bus from Alajuela to SJ near the shopping/downtown area every 30 minutes or so).
This probably does not fit into your timings, but if you don't have too much luggage, there is a small mall a 5 minute taxi ride away ("International mall" I think). They have a movie theater, but I'm not sure if they're dubbed or subtitled (I'd guess the non-children films are probably in English with Spanish subtitles, but can't say for sure) so check if you decide to do that.