Speaker upgrade for classical music

You should be considering a three way floor standing speaker of some type if you are playing classical music. I still have in storage a pair of Focal Electra Be speakers I used to have in my
TV and listening room in my last home. I had a larger listening room; a little larger than yours -and with a 200 Watt McIntosh amp driving them I was able to enjoy pretty much the entire sound spectrum. 
    By the way, I live in the Phoenix area and could even set up the speakers if you were interested in listening to them. I am planning to see the Focals later this month, so you could have first listen to them. 

Second the Sonus Faber recommendation.  (They also look great, if that is a consideration in your family.)

Warm Greetings ssmaudio,Give Brian Herndon a call at Herndon Audio in Albuquerque.He has golden ears.  You can demo Magico and other speakers there in Albq.  I have purchased demo high end cables from him and he gave me great prices and was easy to work with.  I worked on the phone and on email with him.
Leon, formerly of Santa Fe for many years now rural Iowa

Here is my vote for Magnepan or Harbeth too.  I have owned serveal pairs for both over the last 30 years.  You might consider owning both.  For large orchestal / choral music use the Maggie's.  For chamber music or jazz use the Harbeths.  Magnepan's are terrific bargains and you don't have to go to the top of the Harbeth line to get a fantastic speaker - or - consider buying used.  Listen Up in Albuquerque carries Magnepan.  I have been a customer of Listen Up over the years and can recommend them.  You should go listen to Magnepan before buying them - they are not universally loved.  Good luck! Happy New Year!

If you are serious about having a system that could accurately reproduce classical music then you need to start from scratch. That means get a new amp, source etc. The easiest way is to get a one box solution with an integrated amp and a decent streamer. As such you’ll need to first decide on speakers and then pick an appropriate amp. However, it gets more complicated. Classical music encompasses everything from solo instruments to a full scale symphony. It is very difficult if not impossible to get everything to sound accurate and recreate the massive scale of a symphony for less than 50k. This could take years of trial and error to get right. First you need to Read more on this forum, this topic has been discussed to death. 
I listen to classical almost exclusively. Over the last 8 years I’ve had multiple speakers amps etc. Ultimately I ended up with two systems, one powerful system for large scale works and a smaller system for solo piano, violin, trios quartets etc. I couldn’t do it in one system no matter how hard I tried. 
Speaker Recommendations here that worked for me include: Harbeth, Sonus Faber, Vienna acoustics, Totem. A speaker that wasn’t mentioned is Triangle, a horn loaded French speaker. The amps have to be specific to each speaker. 
My current system for symphonic works and concertos : Sonus Faber Elipsa SE  with McIntosh gear MC452 and C2600. 
System for solo instruments and vocal: Diapason adamantes speakers with Mastersound tube amp. A tube amp is absolutely necessary for strings and piano to get right. 
If you can only have one system, My recommendation is harbeth 40.2 speakers with a nice tube amp. I know your stated budget is 8k and I also had a budget of 5k initially. If you can budget 8k on a speaker that usually means you can spend at least twice as much if not more. I got some of my equipment used on audiogon for 50-70% off msrp. So everything is possible. 
Looking at audiogon right now I’d recommend SF elipsa SE, which you can get for around 9k (negotiate) and Audio research integrated Tube amp, GSi 75. It has an awesome DAC, preamp, and phono stage. All in one box. AR is very reputable company. There is one here for 10k, which you can probably get for around 8,5k if negotiate correctly. 
For a source You’ll eventually want a turntable but don’t need to rush into that yet. Get a decent streamer like blue sound node and use a good dac. Send me a private message and I’ll send you samples of my system sound.