Yes, your Canadian bank should agree to cash the € cheque via correspondent banks. And it does take a while for the cheque to clear, but as you said that isn't an issue for you. However, last time I had an international cheque processed, the fee was something like C$50 in total (I am with CIBC).

I would recommend that you take the cheque to a branch of the issuing bank while you remain in Italy. Despite not being a customer, if you explain your situation, I expect they may well cash it for you.

It's my understanding the two black lines/barrato (which is also done in the UK) is an indication the cheque is non-endorsable, not that it has to "go into a bank account".