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I'm not sure about upscale, but when I was in Sofia I was told that I could trust Yellow taxi. That I probably wouldn't get scammed by them. They also seemed to have newer and bigger cars. I'm not sure if they are in Varna, but I think so...

In Varna, the cheapest are Hippo taxis.  The biggest firm is Triumf which has a very handy online app to book a taxi.
Lacia and Omega used to be ok.
I only use Triumf now due to the ease of the app.

Triumf

I was ripped off by this company. Also, their cars often seem shabby.

When I am in Varna with the kiddos (4 and 1 now), I tend to try to use the buses instead of the taxis, as I consider them a bit safer.

When not with the kids I use Triumf.

The idea situation is to find a driver you trust and get their direct number to call them.

That makes sense.

Once, I went on a round trip journey that should have cost about 7 lev. I was going to give the guy 20 any way, but at the end of the fare he quickly pulled out an old receipt  he keeps for foreigners that said 16.80 lev. I looked at him for a second, gave him the 20, and walked away.

Jerkolla...

The thing with the bigger taxi companies is that you at least have a chance of compensation....there are always gonna be the chancers /rip off attempts...but with companies like Triumf you can report them whereas a one man show, you have no chance.