The average cost to level floors is $1-$4 per square foot. Don't panic. The "average" is $1.50 - $2.50. A "little bit" of work is $1/sf. A HORRIBLE subfloor = $4. That is the range. Just for fun, I would budget $3/sf and be happy when the price comes in a little closer to $2/sf.

I always caution homeowners when carpet is being removed. What you are experiencing is NORMAL for carpet. It ALWAYS hides weird things. it would have been nice if you had been warned about carpet's ability to hide bad subfloors (it is part of why they are installed in the first place) but many sales people are less then knowledgeable than installers. And there is no way to judge a subfloor with carpet sitting on it. No way in the world to know if it is flat or not.

Be happy that your installer stopped and mentioned what they found and what needs to be done. Many would simply throw down the vinyl and hope you don't notice the problem until their labour warranty runs out.

Once the subfloor is level, you NEVER have to worry about it again! If you ignore it and put in carpet again (you don't want to do it...so don't do it), you still have the same issue in 10-15 years when you remove the carpet once again. Same issues with sheet vinyl. It will hide the problem but it won't fix the problem.

Sheet vinyl, as handy as it is in kitchens and baths, is tricky in large areas. The seams get themselves into weird spots and the extra you need to order to get a whole sheet used in a single room can add up quickly. Today's sheet vinyls are very realistic...but not everyone is overjoyed with the idea of using sheet vinyl in bedrooms.

Bit the bullet and level the floors. Once done you can have anything you want and should never have to worry about it again.