Solid Hardwood, Engineered and Laminate Flooring - floating floor prep-use of shingles as a leveler

I am installing a floating floor this weekend (kahrs) and I have 1/2 plwyood with 5/8 particle on top of the joist(16inch on cnter).
Since the floor is not perfectly level, I have about a 1/4 dip in a 4 ft span and about a 3/8 dip in a 6ft span in areas of the room, I was wondering if I could use shingles and felt paper as the build up for these areas?

I cannot find a self leveler than can be put over particleboard, at least not in any of the local stores or builders supplies, hence the use of shingles. I know it can be done but my concern is would the shingles leave that "tar" smell in the room once its done(really my wifes concern-I told her it would go away in time)
Thanks in advance for the replies.

Remove the particleboard, it's junk and is not a suitable substrate for anything.

Find out what is causing the dips or sags and fix them. That may mean adding support members between or along side the joists.