Might try a tube preamp

Want a Freya, I’ll gladly sell you mine with the best sounding set of NOS tubes for it. That said, for the money, I would go with the Don Sachs 2. He’s no longer doing crazy combinations of things to them though. He’ll find and match the preamp to the impedence of your amp, and he’ll install an input for balanced cables, but he has tried about every tweak known to man now, so he won’t use Billy Bob’s wang dang output caps or other things that would please customers but degrade the sound. If you have speakers a tube amp can drive he also sells an amazing amp, and both would be under 6K. Not the 5 you spoke of, but it will blow most if not anything under 25K away, and a lot of gear that sells for more. That, or I’ll sell you my Freya with unused original tubes, Ken Rads and early 40’s Raytheons and a PrimaLuna Prologue Five, which will almost certainly sound better than your current setup, though the amp is underbiased so it only puts out 36 watts I believe, but I’ll sell both for 1600 shipped to the lower 48. I obviously went on to higher end gear, but if you start here, you can probably get your money back if you upgrade later. That said, I still second Don Sachs’s gear.

You cannot go wrong with a Prima Luna Dialogue Premium or any Conrad-Johnson that you prefer. Tubes are great!
Rollin

It’s clear from your post that you are new to tubes and your intent is to introduce tube sound to your system to see it’s right for you.

My advice:
1. Buy a tube amp to fully experience tube sound not a tube preamp to use in front of a SS amp.

2. When moving in the direction of tube audio for the first time do not buy new, buy preowned.

3. When selecting a tube amp be aware that the equivalent sound/usable power ratio compared to SS is about 4:1 meaning a 200w SS amp can be replaced by a top brand class A 50W tube amp.

Check out the pre-amps from Backert Labs.  Well within your budget, great build quality, and they sound fantastic.

@bbreneman1   +1 for the Backert Preamp; I use the Rhumba 1.2.

Excellent sounding preamp that's highly tunable based on the relatively inexpensive 12au7 family of tubes (uses a pair). Highly recommended!