Hi,
As I mentioned before, it is quite simply in theory.
That link to the SS Relays didn't work for me but looking at some of the products on that web site, they could work. I see they have special configuration relays that can run to 100 kHz which is probably more than you need.
It appears that the standard relays are rather slow and this may cause problems but I also think this approach may be just as simple or complicated (depending on point of view) as using a buffer chip. The only thing you save with the relays is the pullup resistors/
The more I think about this the more I think my original suggestion of the SN7407N type chip would work as well or better and be a lot cheaper: ($1.00) for the chip that can handle step and dir for 3 axis, 2 pullup resistors per axis, and a couple of inexpensive capacitors on the 24V power supply.
I'd also recommend isolating the PP from the 24V with more than just the 7407 or the relays and would use HCPL2531 optocouplers These are very fast and are only $2 each with one per axis .
I did not think it through carefully but I also believe the CS Labs Universal Converter (the 63 Euro one - differential TTL to OC) could handle everything if configured as an open collector output. Not inexpensive but almost a complete solution rather than a bunch of parts.
Graham