I have a slightly unrelated question and I'm in need of advice: I'm about to work on a grant, with another PI at University of Sydney for a project we've worke

I have a slightly unrelated question and I'm in need of advice: I'm about to work on a grant, with another PI at University of Sydney for a project we've worked on for four years. This grant is to advance our mission of building software system for supporting personalized bacteriophage therapy. Essentially, we're building software to make personalized therapy possible in this space, so we're building something critical for the project. We're building the software to get funding to "phase 2" which is 50x (8 figures) the amount of money the grant's already received. Currently we're employed on the project as contract researchers, but we (and our PI) wants us there in Australia in person. Since we're based in the US/Can, we need to get work visas, which require us to be employed by the grant directly. My question is: we have to sign employment agreements for the university, and our contracts look very much like the "we'll take everything you own, including your ideas you came up with in your shower at your own home" kind of contracts. We've already pushed back and laid out our position — we want to be able to continue building this project past the length of employment and past Phase 2, whether we get it or not. I don't really care if they get full, perpetual license to whatever I create there; it's most likely going to be OSS anyway. I just don't want them to prevent us from using it or OSS-ing it in the future. Has anyone else dealt with universities and institutions in this manner? Do they usually operate like companies in this way?