Where do I go from here?

IMO, if I had your choices and equipment I would replace the Klipsch speakers. There are many, many more choices and would change your sound if you chose the type of speaker you want. If you like the horn sound, look at Volti Audio, maybe the Razz or Rival. But really ribbon speakers or so many otherrs might interest you. You would have to plan road trips to audition some and that could be fun. That is exactly where I would start.

Congratulations. Sounds like a great move. Over the last five years I helped a friend that realized he wanted to finally get into high end audio in advance of retiring. He is now about your age and very happy.

First. your room sounds great. It is not an issue. Over time you can treat it to get the best out of it.

I recommend your first step is to set a direction. I would take your time on this. Consider what you have now as your reference system. You want to experience the spectrum of sound types and find what you want in the long run. As we get older, we learn more about sound and I think for most of us we gravitate to a system that communicates a deeper emotional connection with music. More so than the loud and bass heavy dynamic of our youth. So, don’t put too much emphasis on what you remember.

Go to a dealer and find a few audiophiles in your area. Listen to the best they have... and you want to hear contrast with your system. There is high impact ( the muscle car of systems) like B&W / MacIntosh, highly detailed fast Magico / Boulder... there are natural musical systems like Sonus Faber speakers / Audio Research and all sorts of systems in between. You want to listen to really good ones in each category. See what you are really attracted to... careful... highly detailed / impactful systems can be fatiguing and not musical. Then later you worry about what you can afford. Maybe travel to listen. You want a direction... then you can start swapping equipment.

Just a note. I am 73 and been pursuing this for over fifty years. You can see where I landed under my user ID. I slowly gravitated to more musical / natural sounding tubed equipment and speakers. Not an uncommon destination for mature folks. To help, what kind of car do you own? If it is a corvette... then look at B&W / MacIntosh... I have a Lexus... so for me Audio Research Sonus Faber. Porche... different system... Subaru Outback... different. The sound you like is typically a reflection of your personality.

I think you got good advice from @ghdprentice 

I would do a lot of reading and a lot of listening if you can before you dive in too deep. That might save you from making two or three upgrades instead of one if you can get it right the first time. I’m not sure I would go for an all in one device unless you are absolutely sure that’s going to be your endgame for quite some time. Separates give you more flexible upgrade paths. You seem to be pretty open minded about what path this takes, which is a good thing. Try to listen to various components that present different sound signatures so you can determine what really suits your taste. I wouldn’t just buy a brand or a model based on a recommendation. Try to give yourself options. 
As you move forward with this, I would keep room treatments pretty high on your list as your plan comes together. That’s something I resisted for a long time and that was a mistake. Getting my room properly treated produced more improvement than most components I bought.

good luck and keep us posted

These days automatic turntables are as good and sometimes better than belt drive but a lot of people are stuck in their ways and don't believe it. Buy what you can afford and what you'll use. If it's too much of a pain to set up and play records, you'll probably be less likely to do so. 

The audio quality I have right now is the best I have ever had in my life, and I am loving it!  Full stop.  Work on the room. Don’t change the system.