I just called up the visa assistance centers of both the Finnish and Italian embassies here in my country. These are what I have learned:

1. I cannot have 2 simultaneous valid Schengen visas at the same time in my passport.
2. Italy visa takes 15 working days, minimum, to process
3. The gap between my arrival from Finland and the departure for Italy is just 15 days, it's too wide a gap to be issued an extended visa to cover my Italy trip.
4. There is no expedited visa processing for Italy visa.

So, if I'll apply for a Finnish visa first, I cannot reapply again for an Italian visa since I will have a valid Finnish visa in my passport. And definitely, I cannot apply for the Italy visa first.

If I'll apply for a Finnish visa, go to Finland, then apply for the Italy visa once I arrive from Finland, my visa/passport won't get released in time for my trip to Italy since it's less than 15 working days.

What I am thinking now is, try to apply for the Finland visa, indicating my trip to Italy, and requesting for a longer visa validity. If I will be granted extended visa, then all's good.
But if I won't be granted an extended visa, I am thinking of cancelling my trip to Finland so I can apply for my visa to Italy. But since I cannot have 2 simultaneous valid visa's, the Italian embassy might not give me a visa for this trip?

Can anyone suggest anything for my visa problems?