Are there any bookshelf speakers that sound good on a bookshelf?

Give the ProAc Tablette 10s a consideration.  Sealed cabinet, and very happy to be placed near boundaries.  And sound great. 

I recently auditioned a pair of Audionote speakers purposely placed on bookcase shelves to demonstrate how well they worked and I must say they sounded fantastic. The room was aprx 16x25x8. 

I had a pair of Focal Aria 906's that I used in a true bookshelf environment and was quite happy with the sound.  They are way below your budgeted investment level, but, are very pleasing to the ear.  I used them with a pair of smaller subs placed elsewhere in the room, but honestly they could produce plenty of bass by themselves.

I was fortunate enough that the shelving units upon which they sat were pretty close to my ear level, and, they are front ported so I had minimal concerns with the rear wall placement.  The nice thing about them as well is that they had quite a lot of sound disbursement and required little to no toe-in for proper sound at my listening position, another plus for them since there was limited space in the shelf for them to be rotated. 

Tune Tot by Wilson made for the very purpose that you are referencing ...

Vandersteen VLR CT.

Had a pair for about two years now and really like them. (Paired with Ayre integrated.) They are especially good at low to mid volume listening (about 85dB and below.) Room is 20x14. In fact, I plan to go Vandersteen when I step up to floor-standers, based on my experience with the VLRs. Exceptional.