“An ounce of prevention”. Safety and insurance needs trump cosmetics.
Its wise to pull the permits, get inspections, use approved labor etc.
You can always start enjoying the game room before it’s finished too.
I’m sure everyone here has gone over budget. The game room you deserve or of your dreams may be hard to obtain initially, but you should certainly protect your investment.

Dricore installs easily, you can use self leveling cement and/or tapcons to help level your floor. Roxul insulation helps with sound and is fire resistant etc etc.

Hate to see any unfortunate event happen and then have home insurance voided by unapproved and not-to-code construction.

My two cents

My concrete floor was well poured when the house was buult, but still had lots of “valleys” after the floating dricore floor went in.
Walked on it, marked any bounces, tapcons went in.
Best investment I ever made.