Looking for a new integrated amp

All of the amps you are looking at will work fine with your system.  I think I would go with the Rogue.  More importantly I would take a look at upgrading your phono stage.  Just about any competent amplifier will drive those Tektons, but you will really notice a difference with an upgraded photo stage.  I am not familiar with the Zyx carts, but I know they are held in high regard.  If you have an amp that works, I would ask around to get recommendations from some Zyx owners.  Sutherland Engineering might be worth exploring.

For $2k I wouldn’t do any of those.  Research research and research some more.  Buy used.  A well built amp is going to be reliable, especially if it isn’t too old.  Check customer service as well.  
I was contemplating a Musical Fidelity M6i, a Kinki Studio EX-M1, a Primare I30.  Creek is supposed to be good as well but I couldn’t use my spade connectors on the creek.  I also looked at Vincent and Parasound but thought they were more in line with my Anthem than companies like, Belles, Creek, Hegel etc.

I ended up going from my Anthem I225 (with upgraded fuses and powercord) to a Belles Aria Integrated.  The Anthem I225 is a great amp for the $.  Lots of muscle, pretty refined and smooth.  The Belles absolutely destroyed it. Waay more open and with better bass control / definition.

The Aria Integrated doesn’t come up often and will sell within a day or two.  I was actually contacted by another AGon member when I bought mine.  Mine was never even on the market.  The seller contacted me, offered me a fair price and I paid within an hour.

The Belles made me start looking at amps a little bit differently.  The Belles lets you take a little peek inside what the world of true hifi sounds like.  The Belles sounds tube like to me with a touch of sweetness and more oomph.
Anyhow, I’d possibly broaden your search and start looking preowned.  Decide what strengths in an amp you are looking for then go after that amp.  I had to wait 3 months before getting the opportunity to buy a Belles Aria Integrated.  Also, start looking at pictures of the insides of the amps to get a feel for their layout.  Dual mono design?  Size and number of caps?  Quality components inside?  Sand cast resistors (no bueno if you like smooth sound).  Size and quality and location of the power supply.  Binding posts and connections.  Do you need / want xlr?  Class D, Class A/B, Class A, Tube?  Hybrid?  Do you want an onboard dac?

I’ve heard the Sphinx many times (my friend owns it) and I own the bigger brother m6si.  In my opinion the m5si will drive the speakers better and the sound will be well rounded dynamic and detailed.  I went for the m6si for the extra power.  His sphinx struggles to drive his speakers (they are Adam speakers) when he wants to play it loud.  Just an opinion 

Maybe this?  https://www.audiogon.com/listings/lisa69c5-primaluna-prologue-classic-tube

also

https://www.schiit.com/home?gclid=Cj0KCQiA-rj9BRCAARIsANB_4ACk3Dqf1t3Ro_yG2Av1mczEocFbfYzfKzuKgQNAw5...

And these too

https://www.peachtreeaudio.com/collections/amplifiers  Got my son the Sky and he uses it for Spotify

I've not heard the Musical Fidelity; but compared to the Rogue and Creek I prefer my Primare I32. You should be able to get one within your budget when one comes available; which is rare since they sound so good. I had to wait quite a while for mine. I hear the newer I35 is da bomb; but I think it would be well above your budget.

Here's some reading material:
https://www.yumpu.com/en/document/read/3282098/group-test-primare