NB: Example of multiple relays wiring:
(Sorry about the slightly wierd overlapping wiring on the relay side, it's basically three relays in parallel but showing them side by side too too much room...)
This will act in the same way as a single 6PDT in place of the 3 DPDT, but in my experience this way would be cheaper and less confusing only switching the 2 channels per relay. If it turns out you end up not switching central and SW then you can obviously remove the bottom relay (or just use a single 4PDT).
As for 5PDT, I'm pretty sure they'd exist, it's not like you need an even number of inputs, 3PDT are quite common. However, I'd still stick down the multiple DPDT route, it'll just make things easier, I've personally never seen anything larger in a simple pin format, from the amounts of times I've wired something wrong with a larger relay I've just ended up thinking it's not worth the hassle!