Its possible you may be able to get a new o-ring for the steam arm (is it leaking out of the end of the wand or from up inside the machine?)
A machine that takes less time to clean is more than likely to be a super automatic, which is basically buying convenience at the cost of quality of results. So Id recommend staying with a manual machine if youre looking for good quality coffee. Something like a Rancilio Silvia is similar in operation to the Classic but is made of brass rather than aluminium and they have an excellent reputation for reliability, plus parts are readily available. However its still a single boiler machine, and while it will be quicker than the Gaggia (300ml boiler instead of 120ml boiler in the Gaggia, so quicker for steaming) its still hard going for a group of people.
The next step up is the Nuova Simonelli Oscar which retails about $1200, and then the others are $1500+. However theres an Oscar for sale second-hand at the moment with a much much much much better grinder than you presently have (did I say much better? :)) so Id seriously look at that package before someone else grabs it - and they use 58mm filter baskets like the Gaggia so any accessories such as filter baskets or tampers will go straight into the Oscar. Being a heat exchanger machine youll have your eight drinks out in more like 8 minutes!