Pulling up fiber board to install new tile flooring

Question

My wife decided we've had enough of the cheep vinyl tile in our kitchen... She started to pull up the tiles and I came in and started to cut and pull up the 1/4 ply and 1/2 particle board underneath.

The plan is to lay large format ceramic tile (18x24) so we would want to replace the fiber board with 1/2 cement backer so the tile matches the level of the existing laminate wood flooring in the living room. We did not plan on removing the kitchen cabinets for this.

My question is: should I cut the fiberboard up to the cabinets as close as possible and butt the new cement board up to the cut and tile over it (will that cause issue with the tile over the seam?) Or what are my best options without removing the cabinets?

View from the kitchen towards the living room

Same view marked up with proposed cuts in fiberboard

Original Subfloor -> Fiberboard -> glue -> 1/4 ply -> vinyl tile cross section

Answer 1

should I cut the fiberboard up to the cabinets as close as possible and butt the new cement board up to the cut and tile over it (will that cause issue with the tile over the seam?)

As close as possible is fine, and even an inch or so will be fine, especially for tiles that large.

The only problem i would try to avoid is having the grout seam fall on, or near, the joint/seam where the cement board meets the particle board

For under the toe kick of the cabinet you can rent a Toe-kick saw that will give you a cut very close the the cabinet.