Where to start upgrading?

that upgrade path can be sometimes tough to figure out. Used to have nearly the same HP system as the OP. You can start with the table and cart or the HP amp. You should be able to hear the improvements as make the upgrades. think there are two paths you can go. Start with a better HP amp like the quicksilver HP amp. Then go to a technics 1300 or 1200G with the cart of your choice. Instead of using the Denon cart with the Zen phono buy a decent SUT and run the Denon into the MM stage of the Zen. 

There are a lot of wonderful tube headphone amps out there and I've had several - Woo certainly makes some great ones in varying price ranges, and I've had that Quicksilver HP amp that @johnss mentioned; great bang for the buck, that is! But there are also companies like Ampsandsound, Decware, Donald North Audio in the US, and Auris Audio and Feliks in Eastern Europe who make great gear worth investigating (though Decware and DNA have long waiting lists). WE 300B tubes are also excellent.... I even drive my Susvaras and Modhouse Tungstens through some of these relatively low wattage amps and they sound just fine. 

As far as two channel in listening goes, I’d look into acoustic treatments before upgrading components.

I agree with the recommendation of upgrading the headphone amp first and going  the tube route would be my personal preference as well.  I really, really like the Decware CSP3 headphone amp/line stage preamp.  You can find used examples, if you are patient, for under $1500. I also like the 300B units as well.

Then address the turntable/cartridge/phono preamp.  And don't skimp on the phono preamp, it can be the most important part of the three.

And to not add to the upgrade paralysis (lol), a few other suggestions/things to not loose sight of...

• You didn't mention cabling, but you can cripple a system with cables that aren't up to the level of rest of the system.  That includes interconnects, power, AND the headphone cables. 
• Make sure the headphone amp can support the higher 300 ohm impedance of the HD 650's.  Most good amps should be able to handle it.
• How noisy and stable is your AC power?  Do you need a power conditioner?  
• Are you using any digital sources?  Streaming or CD?  If so, how is that going to impact things.
• You mentioned that 90% of your listening is headphones.  So, don't forget and loose sight of the other 10% that you may want/need to integrate into the system.

In the end, take your time, do your research and plan out the upgrade path.

... just my 2 cents... 

- Jeff

i think ghdprentice is right.

The synergy headphone /amplifier was very hard to reach for my K340...

I dont doubt his choice for driving  headphone picking the last model of Woo...

It is out of my budget as are  High end known headphone...

 I am lucky because the K340 was AKG flagship and with a unique design...

 The only amp i use with it is one of the Sansui alpha one of the best amplifier ever designed by  the Sansui  company before his death ...