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

Fritz carrera be worth a try !

Monitor Audio Gold 100's awesome imaging, clean and punchy.

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.