You are so right, very much below the radar there is a lot of microlight activity. Most small planes right now are in the LSA class, which in Italy is limited to 450kg MTOW (1000 pounds), and that's where the growth is. There is much less GA going on it Italy these days, but still there is some, and they too have moved to the "aviosuperfici", which are licensed airstrips. In most airports landing fees are due, and so GA planes have left airports in a lot of cases, and have migrated to aviosuperfici.
Stupid regulations and poor support of GA have come into effect, and the net result is that a lot of GA activity has moved to microlights. I myself have done exactly this. And I do more "serious" flying when I am in the US and want to exercise my IFR skills or overfly LAX on a C172.
Still, GA is there in Italy, though the numbers are much smaller than they were when I took my PPL 20 years ago. And I have to say to this otherwise my friend African Eagle will punch me in the face next time we meet!
You are more than welcome to take your Luscombe to Italy. There is no problem whatsoever if you only fly from aviosuperfici or uncontrolled airports, thought the latter sometimes have landing fees, yes, even uncontrolled airports can have fees!
Getting in and out of the country is a snap, as Italy is part of the Schengen agreement. You only need an ATC flight plan when crossing the border from France for instance, and that's it. And you can open it and close on the phone, in case you can't have positive radio contact with ATC via the handheld radio.
Glad I could be of some help! Looking forward to meeting you in Italy sometimes!
Ciao, Luca