Would anyone have had any luck running a relay via mobile broadband in Australia?
Sounds likely to be $$$ for shit performance / TOS, but if it's the only / guerilla / rural connection you've got... ok. Typically that backhauls to points coastal anyway, where other fine hosting services are offered, though perhaps not available from the same telco / satcom carrier / network, which might then be anti-diverse, or if available, could be pricier than the competition.
The DirPort 9030 and the ORPort 9001 are blocked.
Those are changeable to whatever is not blocked. If nothing is open, well...
Is it impossible to work around the port blocking?
... a block is a block. Either get it lifted, or vpn / shell / proxy / tunnel around it, or tell them you took your money elsewhere.