This is what I suggest as pre-requisites
1. Figure out the niche you want to target them, if general is your target then you'll have to put more efforts in pitching ofcourse. I suggest, goniche by niche; this way you'll be able to track who's left and who's done too.

2. Clearly devise and define your partnership offering, that what exactly are they going to get if they partner with you and vice versa. What value are you bringing to their table and how are you easing out their pain points. Leave no ambiguity and if possible, make it as a resource on your web page and let anyone view that (and point your prospects to that resource) this way they'll know it is more authentic since its public.

3. If this strategy of yours is critical to your biz then I strongly recommend putting a dedicate person or a team to execute this on daily basis as a project. If full time hire is costlier at your location then hire a virtual assistant (trained on data extraction and social outreach etc).

Now the methodologies to find software companies in Sydney -
- A simple google search with different keyphrase combination will be your first bet. You find a company on google, then find their decision makers on linkedin and send them inmail or connection invite with a short note describing what you're looking for.
- Do give them a call to action wherever possible.
- A search on portals like clutch.co for software companies in Australia will give you great results of companies who are very active in selling/ branding themselves and they make a better prospect for you.
- A direct company or executive search by using linkedin location/ industry and keyword filters on premium profile will help too.
- Do exploit local Australian biz directories too, they are similar to clutch and linkedin but more precise for Australian companies.
- Keep talking to people, the more you speak and listen the more you know and be able to shape your offering in a better manner.
- Keep your partnership offering document straight forward, quick to read and absolutely unambiguous.

I hope this helps and I wish you success.