I'm with you on the draft. I think that is a pretty good example of something that is antithetical to freedom. But even so, you qualify it by saying its fine when the country is being invaded. I actually disagree with you there - it is always wrong to force someone to fight, regardless of circumstances. Their life is not the governments to decide - it's far too important.
As for non-coercive methods, I'm all ears. I want to see huge investments made in adapting internet technology to secure voting. And I'd much prefer something that wasn't coercive. However I do think that this issue of non-participation needs to be addressed sooner than later, and mandatory voting really isn't all that hard to implement (in Canada anyways - I personally think it would be impossible in the US).