Cartridge recommendations

The Benz wood body series is very nice and gives some of the warmth you might be after. You'll have to check price and maybe accept used if you are comfortable with that.

I second the Benz Micro wood cartridges, I have an LP which is a wonderfully neutral cartridge, but just on the warm side of neutral, as opposed to the Zyx Airy 3, I used before. Unfortunately, they seem very expensive in the US, compared with Europe.
Another thought is Koetsu. I used a Rosewood signature and now a second hand Onyx, both great cartridges. It is very hard to choose between the LP and Onyx, so I am keeping both, long term.
As Chadlesko says, do'nt be afraid of second hand. Retipping Benz's is fairly cheap, Koetsu's not, but you effectively get a new cartridge. As a cheaper option, try one of the smaller retipping companies. The Expert Stylus company in the UK, provides a first class, reliable service. They have been in business over 20 years and I have never heard a bad word about them. Recently retipped my 2nd hand Koetsu

Another good choice for tube phono like your is the Grado Statement Master 0.5mv
Great mids and a well balanced sound
I'm just selling one!