Most SWAT teams have standardized sidearms, so I'd be surprised if you can carry your own. Assuming that's not what they issue, I'd shy away from the GAP. As mentioned, it has no benefits over a .45ACP and is pricier and harder to find.
Try a Glock 21SF which is a .45 with a slimmed down grip, it'll be wider than the G38 but not as big as the G21 (though only barely). If I were planning on being a SWAT medic, I'd find out what my team was issued and purchase that model, assuming you aren't issued one. Crown Point, Indiana? I think it'll probably be a Glock 22 .40S&W but I may be wrong. (I'm a hoosier, too)
In short, a Glock 38 is the way to go if you want a .45GAP, but I wouldn't suggest a .45GAP over a .45ACP in any circumstance, especially since the G21SF is now available.
TRL