the mast is probably grounded, so you'd still have just a shorted
antenna if you connected the center to mast.
I would dissconect both from mast and spread inner / outer apart and see what happens. generally this isn't good, and you need to actully strip the sheild away as it's blocking the center wire.
I would also just try put a ~14awg
single wire in the back of the
antenna jack dangeling and compare it. often that's all you need.