Welcome to AFF,
I had a quick search and there are saver two business class seats (190,000 less 15% if you book online, total cost for two people) for 4, 5, 6, 8, 10 May (I only looked at the first 10 days of May) so there appears no issues getting to Europe early May.
On the return from MIL?, which I assume you are referring to Milan which correctly is MXP, I could not find any saver seats for the last week of May, although there are several other cities nearby which you could easily access, as dajop mentioned, such as Zurich, Rome ... also further afield such as Paris, Frankfurt, Barcelona.
Throwing this into the mix, it's a bit further but probably worthwhile is if you fly out of AMS. Flying out of AMS means you pay 160,000 points versus 190,000 points for other European ports. There are two business class saver availability ex-AMS on 27/5 and 2/6 if that could work for you.