Uphill battle because yes, you have already been denied AND because of the work history pattern AND because you are at a disadvantage compared to most 2nd time applicants. If you proceed as if the only reason you weren't successful before is because of the work record, you'll end up lengthening the process...

Usually someone applying for the 2nd time knows what all the issues are why they weren't successful because they've been through the 5 step evaluation. You were cutoff at step one.

Call your local office. NOT the national 800#. See if the online application was accepted or not. If not, ask to have a paper version mailed. I believe that's still available. If you must choose between applying online or in person at the office, I would choose the office. Either way they follow up with additional paperwork.

Have you attempted to find a local non attorney SSDI representative? They often have worked for SS and understand the process and what will be required. They are often willing to help at the initial application stage.