You can also always fly to HEL on LH (may be lot cheaper) and take short hop to Tallinn on Aero Airlines/Finnair or
www.copterline.com (ships are about 10x cheaper and crossing takes 4 hours). Distance between Helsinki and Tallinn is only 80 km.
If it is acceptable for you to collect Eurobonus points instead of M&M miles, you may want to call to Estonian Air and inquire about fares from Hamburg to Tallinn. Estonian Air started with "low fares, all frills" concept on Moscow and Hamburg routes and prices ex-Tallinn to Hamburg start from 700 EEK o/w (about 44 EUR+tax). Unfortunately I cant find same price from HAM to TLL.