yep – I reckon you’ve got a lazy avoider as strata manager 
– (I’ve got a slack one in mind but don’t want to get sued for libel) – if you don’t already know who’s on the executive committee(EC), ask around – then approach the friendliest member to put your case.
question – do you have tiles or other floor covering – in which case they might argue that part is your cost – but damp to your walls from above is definitely common property/strata responsibility – anything below the surface or paint is generally common property.
to save the $800-1000 report you could get 2 or 3 opinions from builders or tradies to have a look and give you a quote for fixing it – without seeing it if it’s concrete floor I’d imagine a skim coat of concrete to change the fall – but watch for dampcourses so you don’t breach those – an alternative may be to dig/grind a trench to divert the flow
that way you’d have some cost information to save the EC time and deliberation about the $800-1000 report – e.g if you can get a guy to do it for $500 then that could look like a no-brainer decision for them to make on the spot at their next meeting.
or – if like our EC where I’m a member – by email discussion/decision, they could instruct the strata manager to have the work done, as soon as they have the various costs in front of them – that’s where you could nudge it along as above … 