Which direction should I go?

If you can live without a lot of bass (or would consider a sub or 2), I think you will get a better sounding bookshelf speaker. There are a lot of great options at the sub-$2k level. The ones that have caught my attention (and which I hope to audition eventually) would include the following:

Nola Boxer
Harbeth
Fritz Speakers

If you want to got the SET route, then you will need something very efficient. And there are some nice efficient speakers out there. Tekton & Zu would both be worth looking into. And for a

What are your current speakers? You may well be able to make a nice improvement in your main room system for a lot less than $2K. Many people swear by Totem speakers with Rega electronics, and Rega's own speakers are excellent. Second-hand Totem Arros or Sttafs or Rega RS3s or RS5s would all be well under your budget.

My current speakers are Beta Infinity 40 towers. They have decent clarity, but lack involvement. They were always meant as a stand-in. I haven't had time lately to listen a lot, much less audition upgrades. So, hence my thinking is get something right now that is a nice upgrade, but not have the pressure of making the *right* choice, and then tinkering a lot with electronics, cables, etc... (not that I wouldn't rule out a new amp, but for the sake of discussion let's say it's the Rega for now).

As to your suggestions Afranta, The Totems look like they need some placement away from the back wall, which I could not accommodate in the family room, but could in the study scenario (option 2). Rega RS5 is on my list to audition as well; I have heard they can be a bit lean, but I'll let my ears decide that. A lot of people like the Monitor Audio RS6, but I did not care for the treble at all. One good plus about option 2 for me would be relative flexibility with regard to placement.

Pay your bills first.

Screw the bills. They can take the house but they'll never take your gear ;)

I won't tell you what to do of course, but if I were in your situation I would get a pair of efficient floortanders and a low power SET for option 2. I think you might be surprised at the Q of sound assuming a small space and listening near field.
I can recommend the several Tekton models between $650 (M-Lore), $850 (new Oriel 10) and $1000 (Lore) $1500 Katz Meow. I own Lores and Katz and those are the only ones I have heard of the ones I listed. I used to own Zu Omens and they might work for you also ($1500), but I personally prefer both Lore and Katz.
Many amps in the $1000 range, not necessary to be SET but that would be my preference.
Good luck and have fun.

Option 3:
You can get active studio monitors Event Opal powered with near 500W each($3k for pair) for your family room. These are very precise sounding speakers that reveal all studio recording details. They also reveal recording imperfections such as unfiltered dubbing! They sold currently on pro audio market (fullcompas.com, bhphotovideo.com, zzounds) but considered to be high definition speakers for the most demanding audiophile needs. They also equiped with room correction controls! I work part time as a studio tech and these made me think that I haven't heard electronics sounding so natural where pre and post recordings sounds the same.