Pushing it to my max on a 7% 2kft climb. I'm cardio limited, but legs never hurt. How do I push it harder?
This type of effort very much comes down to W/Kg at FTP (Functional Threshold Power).  You can get lighter, or you can work to raise FTP.

There is no magic formula to improve FTP, it requires (beyond a basic level of fitness) either a coach, or some well thought out self coaching.  A power meter and knowledge of how to use it is an invaluable tool, but where this is not possible, a HRM (Heart Rate Monitor) and RPE (Rate of Perceived Exertion) can work as an alternative.

A very popular training session is to ride 2x20mins at FTP 1-2x per week.

Self coaching can be tricky, but rewarding.  Pay special attention to making sure your easy rides are easy so that your hard rides can be hard.