Kit suitable for 4x Z560M tubes?

Well, the clock's electronics are compatible with Z560M but there's no way you will be able to get the tubes to plug into the board. Z560M is a 13-pin tube but IN-2 has 11-pins. That's a show stopper right there but also the pin circle diameters are different as are the pinouts etc.

I suppose you could mount your tubes off-board and run wires from the tube holes in the board to the tube pins if you want. Not a fun job but not totally impractical either, especially if you have tube sockets or can make your own tube holder board.

Or you could use the 4 digit Classic kit which is intended for off-board tube mounting, and make your own tube holder board or run wires to tubes as above... you get the idea.
Classic 6 digit here: www.nixieclock.biz/StoreClassicRev6.html and 4 digit version is available if you email Ian.

Or you could buy a set of IN-2 tubes off eBay for relatively cheap, somewhere in the neighborhood of $3 per tube in lots of 6. Trouble with that is that almost all sellers are in Ukraine and given the current turmoil there who knows if they are able to fill orders.

As far as a tube-ON-board kit that fits Z560M, to my knowledge there isn't one but there's a chance I am mistaken.