Long response.
Don't bother spending up to $2k, as you may not be happy with the results of putting the speaker box inside the bigger furniture box. That is the physics of what you are attempting to do. The issue is that speakers need some room to breathe.
Placement inside a bookcase negates some of the audiophile niceties like soundstage and speakers disappearing in the room. Music can be moving and sound clean and accurate, but that will be as far as it goes. You may or may not need a subwoofer, as the bookcase will usually reinforce the bass.
I have spent more than 20 years attempting to make this type of speaker placement work. I was always afraid that my cats would knock the speakers off their stands and hurt themselves. I have used acoustic suspension (sealed box), rear ported, and front ported speakers. Spending more on better speakers didn't give better results.
So, what worked best ... Rega Aras (now the RS1), Ascend Acoustic Sierra Monitors, and NHT SB2 (now the Classic Three). What did not work ... Spendor SA1, Totem Mites, EPOS ES11, B&W 302s, and KEF Q55. What were ok ... Energy RC10, Wharfedale Diamond 8, and Omega Super 3i. The amps used were the tube Prima Luna Prologue 2 and the solid state ADCOM GFA 545 and Outlaw RR2150. The source was primarily CD.
So from my experience, the placement of the port was not the critical bit. Speakers that were designed to work close to a rear wall and/ or on their sides sounded best. As you can see, lots of trial and error. Speakers that have a generous return policy may be useful.
An alternative worth exploring ... place the speakers on top of the bookcases. I am doing that now with my Ascend Acoustic Sierra 1s and they sound much better than inside the bookcases.
Rich