Cellulose is heavy. It will compact the batts, and as it settles it will compact onto itself as well.
You would get a better R-value, that lasts, if you blow in fiberglass insulation. It sounds horrid, but it does not make you itch like you think it might. It does not compact down or form a crust. It is not dusty as you blow it in, like cellulose is. It is much easier to work with.
The only drawback is, since it does not crust over, aggressive air movement in the attic can push it around. That is not a problem, normally. Make sure you do not block soffit vents or blow it tight to the underside of the roof.
You would use the same machine to blow in fiberglass as you would use to blow in cellulose. You will find blow-in fiberglass at the same place you buy blow-in cellulose.