you can roto hammer the concrete and secure the flange as needed. Or use a repair ring secured to the floor for the closet bolts.
If there was no give, then what you had was good enough. Sometimes a flange in concrete is there for life. We secure them anyway.
If you attempt to add spaces, something I don't like, goo them up with Silicone. Personally, for the last 40 years the plumbers around here use two wax rings if the flange is low, and it's works out just fine.
Adding spacers has been a real iffy solution. I've had far more troubles with those. I don't even carry spacers on the truck. I have to garantee my work.