Ok I was wrong once again. It looks like I was confusing "focus" with zoom, cause after trying a few more camera apps, they were all able to do the same little "subtle" zoom effect that the Chase quick deposit app was doing. It doesn't actually zoom I discovered, it just focuses better to make the check sharper. I could tell that this was what was happening because when you use a camera app (or the phone's camera app) to focus, your display will do this thing where it looks like it's zooming in a tiny bit, and then all of a sudden it will jerk back. That's exactly what the Chase thing was doing...which is just focusing, not zooming.
Here are the results of all the camera apps I have tried:
lgCamera -- no zoom
eCamera -- no zoom
Camera Advance -- no zoom
Camera Magic -- only zooms at 1600x1200 and below, but it's not a real zoom...it just freezes the last thing you were aiming the camera at and lets you zoom in on the still, just like our phone's camera lets you zoom in on a picture after you take it
So there's no zoom capability on our camera after all. lgCamera is probably better than the phone's camera app btw. And while I was looking for camera apps, I found this app called WarpCam that is sick. It lets you do some crazy/trippy effects before you take a picture, but it locks some of the effects unless you get the pro version.
I already knew there was no zoom before I got this phone, plus most of the zooming abilities of phones I've used in the past have always looked horrible anyway, so it's not a big deal to me. I own this phone for LTE and little else