My water meter is 25 years younger than yours, only I had nearly 3 feet of 3/4" dia. copper between the basement floor slab and the shutoff valve.
Back in 2000, my street shutoff faucet would not close fully so I decided to replace it with a Meuller ball valve. At the time I was told to purchase a MAPP gas torch, as the brass ball valve had a lot of mass to heat up to the point of the solder melting.
After 22 years of use, this ball valve won't close completely, but at least I no longer have a valve with a faucet washer that can break apart.
In your case, I would break up the concrete below your street shutoff valve to expose as much of the soft copper pipe from the street as possible.
To cut out the old valve you will need to saw it off and then clean up the end for soldering.
Based on what I have learned the hard way, a good ball valve like mine won't last forever.
If I had it to do over again, I would solder to my supply from the street an all brass dielectric union, like the one in my photo for my water heater connection.
I suggest the Watts LF3008 3/4" all brass dielectric union (from Grainger) which will allow you someday to easily swap out a ball valve that's gone bad.
This dielectric union has a nitrile gasket which is similar to the gaskets in your water meter brass nipple.
I coated my gasket on each side with silicon lubricant.
Don't buy the half steel/half brass dielectric union which costs a quarter the price of the all brass one.
The dielectric union will require that you bond your ground wire from your electric panel to both sides of the union.
You don't really need a dielectric union, but I just haven't found any non-dielectric unions with a gasket.
I hope that my information helps.