Best Tubes on Market today?

IMO,I don't believe that you can do better than Vintage Tube Services. Andy is great to work with.He also has "Andy's picks" which are thoroughly inspected used tubes .I have never had a bad tube,new or used from him.

I have no clue if this might be your issue or not, but I found that I was getting hum in my headphone system that was being caused by the outlet itself, switched it out to an industrial grade one and the problem ceased. YMMV

+1 for both Andy and Brent J. For the price of some tubes, it’s important to know the NOS tube you get is the tube you want and ordered. I found that the tubes make a huge difference in SQ, particularly in phono stages. For my ears, and the lowest noise I run Amperex & Telefunken NOS. 

I know now nothing about 845s. 

The new PSvane & gold lions 12AX7s have an edge that I don’t prefer. But that’s the fun of rolling tubes. Brent J has me on hold for a pair of Tung Sol 6SN7 for my amp. I always look for military or medical grade “low noise” tubes. 

On the humming noise topic, I had a “motor-boating” sound only coming thru my phono section. After LOTS of trial and error, I isolated it to RFI coming from my google mesh WAP. It was getting picked up somewhere in my TT, cartridge or cables. When I moved the WAP across the room and onto the floor, it has essentially disappeared. So don’t overlook that a possibility. Good luck!

You didnt go wrong with thomas mayer’s, they are really magnificent products!!! 

I've been running 845 amps in my system for nearly 20 years, some noise is inherent to these amps. Relatively high powered SET amp with high efficiency speakers creates perfect environment for creating noise.

One effective way to decrease noise is to use less efficient speakers, my highly modified Merlin VSM are far less noisy than my highly modified Klipschorns.

There is nothing wrong with your amp. As for tubes,in your price range get the Psvane WE Replica, great tube. At a lower price the Psvane TII is very nice. NOS tubes are way above your price range. Shuguangs are decent for the price. I would stay away from Fullmusic, nice sound, not good reliability, Psvanes have nice sound quality and are reliable. My next upgrade tube will likely be Psvane Acme 845.

It is also possible dirty AC could be impacting your system. Power conditioners will be effective here, however, they will likely negatively affect transients with any 845 amp. I've tried many power conditioners over the years, all negatively impacted transients until I tried Furutech. Flex-50 NCF inline filter. This has greatly diminshed hum and maintained transient impact, great filter in my setup.