I recently fitted a Varta F19 battery, the 'best' replacement match to the original A2 battery, apparently. This is 190x175x315 mm and just fits the battery well, with about 20mm length to spare. So no, your proposed 353mm is too long to fit, take a tape measure and see for yourself.
Andy
Edit. I am assuming you cannot use 20mm at the left hand end as the well floor begins a curve up to merge with the side wall and the battery would not sit flat if you tried to use it, but depends on the design of the battery I suppose.