Requirements for upgrading license to 1600 ton master after taking limited exam for 500 ton master

I currently hold a 1600 ton mate with oceans and a mate of tow.

I understand that I can take a limited exam to upgrade to 500 ton master with 360 days under my mate of tow.

But I also see that with 360 days as mate you can upgrade to 1600 ton master.

If I go the route of the limited exam 500 ton, could I not turn around and submit my seatime for 1600 ton master without further examination, or would it need to be another 360 days under the 500 ton?

I believe so, yes.