Why are you over complicating this process? You can not apply directly through the school’s website: it is going to take you to the portal.
The cleanest and easiest way is to apply to SUNY using the SUNY application. Your application is sent to the university with in 24 hours. GC can just approve waivers on line, upload transcripts rankings etc. It is also easier to track your application for compketeness.
The common app actually takes a few days (because it is still going to the SUNY portal).
The easiest way to apply to CUNY using the CUNY appllication. IIRC, CUNY will no longer accept applications through the common app because of what you are doing.
There is no free application for the SUNY 4- year college. You either pay the fee, submit a fee waiver or your application is not processed.