I dont own a Gaggia, but my Mokita has a similar problem in that without the froth enhancer.... the bl*&dy wand is too short >:(.
Ive tried to locate an alternative longer "Silvia" type wand that would fit straight into the Mokita but no such luck unfortunately. So, the only way Ive found to beat this problem, is to buy a swag of different capacity frothing jugs. In my case, it has meant that I needed a 400ml, a 650ml, a 750ml and a 1.0 Litre jug. This is so the tip of the wand can be immersed to the correct depth for different quantities of milk :-X. Yeah I know, its a pain in the proverbial but it works ::).
That way, I just have to use the right size jug for the amount of milk I need to stretch. Matching the right size jug to the various combination of coffee milk drinks on order can be a bit hit and miss sometimes, but mostly it works out ok.
I wish I could find a better wand to fit on to the Mokita, that would solve all my problems :). All the best,