Approaches to moving a chessboard (and holding chess piece with electromagnets)?

I am attempting to make a reduced chess game where the board moves rather than 2 kings.
I have firstly some physical build questions that I hope you might point me in the right direction for.

Here’s a link to a mockup video:

short animation

The scenario is:

There are only two kings in play, both of which have neodymium magnets attached.
They sit on top of a clear acrylic sheet.
Below that is a chessboard (vinyl and acrylic 5mm).
Affixed to the underside of the chessboard are two electromagnets, 1 for white king, 1 for black king.

A small camera is also fixed to the chessboard, so moves with it, giving the impression (via video) that the opposite piece is moving to the one that is. Each electromagnet either goes on or off depending on which piece is meant to look like its not moving or moving.

So basically, in the real world the board moves with one piece.
In the video world it looks like the pieces move not the board.

Each square of the chessboard is 5.72 cm.
If I make the simplest version (where each piece only moves one square, then this is the size of movement I need). If it can move twice then its more like 12cm.

The weight of the board (and the attachments of 2 electromagnets and a small camera) is 900 grams
The size of the board is 48cm sq.

I have a Power HD servo 3001HB analog servo
Key specs at 6 V: 0.12 sec/60°, 61 oz-in (4.4 kg-cm), 43 g.

My first questions are:

If I use a rack and pinion will I still be able to get the board to move smoothly, hints, tips, other sugestions?

Does the servo look like it might be up to the job (considering friction etc) or should I use a stepper?

What might be suitable electromagnet wise - the pieces themselves have small strong neodymium magnets?

Thanks

Kyp

Hmm, 3D printer X-Y table.
What happens if you moving pieces have to pass a square that already has a piece ?

@lastchancename, there are only two pieces. If they end up on the same square, then one of them loses.

Fair enough - I saw that, but expect this may grow in the future!

Then make the squares wide enough for the pieces to pass by each other.