Wow, what a gorgeous bike. Yes, do grease the screws, and NO, don't grease the flat washers inside the shifters. If your problem returns, take them apart again and clean the grease off the flat washers. They work by friction (as the name implies), so you WANT friction between the washers (but do grease the bolts). The reason that those fastener bolts have loops on them, is specifically so that you can adjust the friction while riding.