What do you mean by the screeching thing?
The Gaggias wont run out of steam - the small boiler + high heating power means that the boiler can cycle with the steam valve wide open. The downside is that maximum steam pressure is rather low and the steam power will fluctuate a bit as the boiler heat cycles. It is actually the small horizontal cross section rather than the outright boiler size that limits the steam pressure but this also limits the maximum heat loss rate hence the ability to cycle.
Are you steaming with the bare arm, the plastic stump or the full panarello arm? The 2nd option is by far the best but you will need to raise the milk further up (to about the 0-ring level) as the milk froths up else the steam will start hitting the froth which will cause excessive bubbling and maybe the screeching you are talling about.
Modding the boiler size is pretty much out of the question.