Spending a month's salary

First of all (please don’t take offense) refer to your speakers as "standmounts" not "bookshelfs" its not 1983! Have you demoed the Boulder 866? The mentioned Hegel could be a sideways move when compared to your current Parasound separates. Have you considered the newer Parasound JC 5 power amp? Keep your P6 preamp then upgrade your DAC/Speakers.

I have a $6K DAC and do most of my listening on a $200 balanced one.  

There's that. 

You are correct in concentrating on speakers you like, that you can afford to drive. The room is just as important for perceived SQ.

@tee_dee

Thanks, I probably should have asked if this is an installment, or for the full system.

DAC/preamp combination makes sense. Suggestions above allow you to avoid the extra expense of needing a Roon server. Next, or concurrently speakers.  Many consider the speakers to be a first purchase around which you build your system. If time isn’t an issue, the used market for the above equipment makes sense. Then sell equipment and evaluate your needs.

Audition, audition, audition as much as you can.  If you are close to Chicago, they got the show coming up in April.  You are looking for something for your ears that you like.  You have mentioned a smaller room, so where you are listening, see if they can do a similar set up to what you have, as to a room size.  I have had places move speakers and stand mounts are an easy move.  If they wine about doing this, go somewhere else.  It can be a good indicator that they are or aren't worth dealing with.  As mentioned, hi-fi mixed with mid-fi you may not get to where you are wanting to go.  The speakers have to match the amp.  Some brands to consider and look that I have really liked in stand mount are:  Harbeth, Sonus Faber, various LS35A manufacturers.  Another consideration would be a pair of Meridian speakers, these are speaker and amp as one.  While not a true stand mount, they have a similar floor profile.  Still love my old reliable JBL's.  To me everything has a signature sound and from there match to an amp/components, as mentioned by @vonhelmholtz  

Another point to make.  I used to sell and found myself missing what I had.  While very happy with the new, there is still a signature that makes each great design especially wonderful.  I have become an accumulator.  My wife hates it but, oh well.  You might find you really miss what you had. 

Lastly, there are some that grow a system around an amp and find speakers to match.  For example, smaller rooms are great for a low wattage SET amp with high efficiency speakers, such as Zu.  You have much work and fun ahead of you. 

Your question is which first… definitely speakers.

@hoosierinohio …”audition…”

+1

You want speakers that really appeal to your emotions.

In the long run speakers typically will be between 30 - 35% of system… but no set rule. Most of us do this over a long time. once you have speakers you want to break them in and know what they sound like before upgrading the rest of your system. So, get a few hundred hours under your belt before considering the rest.

All electronic components are equally important. If carefully chosen then Streamer = DAC = Preamp = amp in cost. Don’t think the streamer does not make a Hugh difference… it does. 

So, your interconnects are great until all else is done… and you are recovering from the major purchases. Choosing wires are best done after everything is broken in and you completely understand what your system sounds like.

Be not in a hurry. I remember early in my audiophile days, wondering around listening to speakers for weeks, they all sounded fine. Then a tear rolled down my cheek on one set of speakers… I had them for about ten years. Great choice for me.