So... I do not know of a 3 or 4 way ceiling fan switch. I DO know of a ceiling fan switch, the GE 12730. I have 3 of them (we have no AC so ceiling fans are needed). It works well, controlling 3 speeds. Although it is treated like a dimmer switch (0-100%) by the Almond, so generally setting it anywhere from 1-33% is low, 34-67% is medium, and 68+ is high if I recall.
There are wall switches that can act as "secondary controllers". The idea being you pair devices to them then control the switch to control those devices. Almond does not support secondary controllers so you could not control the devices that are secondary to it (just the switch itself).
There are some switches out there meant for 3 way (or more) situations usually with a secondary switch (not to be confused with a secondary controller). That secondary switch is JUST meant to talk to it's primary switch, never back to the overall controller. You mentioned that in the initial posting about the GEs. I think an example would be the GE 12723. Looking at an Amazon listing for one I can see they are supposed to work with the Z-Wave (or other protocol) switches GE has including the Fan Switches, and they can be used for 3 or 4 way combinations. The problem is the listings (and reviews) mix the various switches so sometimes it is messy. But it looks like you could use the 12723 along with 12722 (Z-Wave on/off), 12724 (Z-Wave Dimmer) or 12730 (Z-Wave Fan Control) to do what you are looking for.
I cannot say how the 12722, 12723 or 12724 have worked or would work (maybe there are other postings for them) as I have not used them. I can say the 12730s have worked very well all along.