Subfloor leveling with cork tiles?

Hi Everyone! We were able to purchase our first home and it's 103 years old. I ripped the carpet out upstairs and am slowly uncovering stories of the past. Under the carpet were vinyl tiles (I had them tested for asbestos), then plywood, and then the original pine flooring covered in lead based paint. I was dreaming of installing Marmoleum click but one room is very unlevel and not flat. A contractor told me my house isn't falling down, just old settling, and carpet is the only thing. I really really really don't want to do carpet for many reasons but I also understand I may have to.... Any experience or ideas for leveling without shimming (not lifting those plywood sheets to expose lead paint), not using a self leveling concrete (too many spots?)... Wondering if cork underlay could be layered at the biggest sags and low spots? Thank you!