AJC – on the assumption that your Plan’s in NSW, I’m afraid that if the Special By-Law that’s quoted in your post was properly considered by way of a Special Resolution at a General Meeting, that it’s Registered, and that the Owners Corporation’s (O/C) decision to deny consent to your proposed works (i.e. the floating floor) was also correctly taken and accurately minuted, then in my opinion you have no grounds to seek Orders or in fact any other redress in the NSW Civil and Administrative Tribunal (NCAT).
That’s not to suggest that the arguments and supporting information that you put to the General Meeting weren’t valid, it’s just that there are few limitations on the ability of O/Cs to make and to enforce Special / By-Laws, and none of those limitations applies to the one that’s affecting you.
As you’ve noted, some Proprietors in your Plan have in the past suffered noise-related inconvenience as a consequence of some activities involving changes to floor coverings in Lots, and the O/C’s Special By-Law didn’t discriminate between Lots; that is those on the bottom residential floor and those located elsewhere.
Noise transmission from hard flooring, and particularly from wooden / floating floors that it appears you’re proposing, is a REAL issue for O/C’s, and previous posts to this forum have revealed many so-called experts that will guarantee anything in terms of their product’s sound insulation capabilities in order to secure a job, and then leave the consequences of non-compliance and neighbours’ complaints to their former client.
Everything considered and given the positioning of your Unit, and taking into account that proper sound insulation doesn’t just apply to the floor, but also to the margins where a hard floor abuts common walls with adjoining units, IF you can obtain the services of a properly qualified and insured Acoustic Engineer who’s prepared to not only specify suitable sound insulating materials for your Unit in terms of a product’s ability to meet a suitable “weighted normalised impact sound pressure level” (Ln,w) [typically <60], and additionally to indemnify you should noise-related problems later arise, then I, for the first time with regard to such matters on this forum, would suggest that you proceed; cautiously.