Here is a crazy idea.........

Since the bathroom has another entrance and it is not difficult for anyone to just walk down the short hall to use the bathroom if necessary, so you do not really need the second door to it from the study. Also in a 4,000sq/ft home you already have plenty of storage places throughout the house you do not need the walk-in closet for everyday continuous access. In fact you would not have counted on having access to it had your MIL been using the room so the closet is really a 'bonus'.

The two doors are symmetrical and evenly spaced on the wall. How about making fake windows out of them with drapery? Have the drapery match that of the window on the other side. This will give you another 'wallspace' and make arranging furniture easier. You could put your loveseat on that wall between the two "windows" or maybe the desk. It would just give more options with furniture arrangement. The closet could be used for storage of out of season things like holiday decorations and would still be easy to access when necessary by pulling the curtain aside.

We don't really need the second door but the house is already built. :)

The space between the two doors is less than 3 ft so not enough room for a loveseat (I wish) and the closet is already in use for school items and related storage.

If you want it to look good from the entry, then have something of interest in the upper left corner. I can see a nice easy chair and lamp for reading. I also have this thing for siting a desk with computer perpendicular to a window, to minimize glare on the screen. It's also good to position the desk and chair so that the person at the desk has a view of the entry.
I would have put a library wall against the wall opposite the door, but you said that you already have bookcases flanking the entry.
So here's my layout:

Alternatively, you could put the desk under the window.

I also think that a half moon table or chest, with a picture or some wall art over it would look good, either between the closet and bath doors (as in the first layout) or opposite the entry (in the second). This will add eye candy to the room.

suero,
Thank you for the layouts! I like the first one and think that will serve our needs best. We wanted library walls all around but could not do that since we thought we were going to need the room as a bedroom; we may still, so this would work best. It may be a little tight next to the left chair. I failed to mention that the builtin bookcases are 1/3 cabinets on the bottom so they stick out more than traditional bookcases.