Less than 60 days notice as a tenant

I’m in a bit of a situation and could really use some advice. I currently live in an apartment, but I’ve found a much cheaper rental in the same building. I gave my 60-day notice to my landlord on January 24th and requested to move out by March 15th, so I can transition into the new unit without any issues.

However, my landlord asked me to originally move out by April 1st and when I told him I can’t, he asked me to fill out an Landlord and Tenant Board form so he can formally capture my request. I’m not entirely sure how this affects things. The catch is that I need to move into the new unit by March 15th to lock in the lower price. If I miss this deadline, I might lose out on the cost savings, which I can’t afford to happen.

Does anyone know: 1. What the LTB form is for in this scenario? 2. If moving out by March 15th could cause any complications with the process?