What to try?

One amp I’ve owned and don’t usually recommend to everyone is the VPI 299D, but it fits your search perfectly. It is more refined than other tube integrateds from Rogue or Primaluna and has a MM phono built in.

It was designed in joint by Harry Weisfeld (VPI) and Steve Leung (of VAS audio). Only 100 of them were made. One is on USAM now, and I have no affiliation with the seller:

https://www.usaudiomart.com/details/649770311-limited-addition-vpi-299d-integrated-with-additional-tubes/

The tube rolling is as extensive as a Primaluna, but has the added tube rectifier which can accept GZ34/5R4/274B variants. It lets out a lovely sound and will be bolder than your Yamaha (I’ve owned an A-S3000). 

For the money, you won't  go wrong here:

PrimaLuna Dialogue Premium Integrated Amp For Sale | Audiogon

User/mag reviews, build/feature/spec -it doesn't get much better.

Everything you need for an introduction to tube amps. Auto bias so you can use many popular tube types for your own "sound"

That VPI amp looks very interesting as does the Octave  I will do some research  I can not find the Pathos @soix  suggested  I know that Upscale Audio is a dealer and importer and has a 30 or 60 day trial but shipping is on buyer   That is another possibility to at least demo one but it will cost shipping if it is not a fit with my Model 5a which are well built look great and sound full  

I went from a LineMagnetic KT88 to Raven Audio and never looked back. Looking to go up in their line next to the Reflection. Details in my profile.

Within your budget, but no phono stage.

They sell direct only, 45 day in home trial, and 100% trade-up value within 12 months.

Why would you want the phono stage built in? There are so many seperate phono stages....plus you just box yourself in with one that's built in. Get a Sugden A21se and be happy...