Very quickly, the price of democracy in a cost-benefit analysis is a strictly different kind of value question than a dollar value question, so it's hard to quantify. But in terms of studies, I'd point to the 1991 Royal Commission on Electoral Reform and Party Financing and Voter Turnout in Canada, by Herman Bakvis, which said that Sunday voting was a clear factor in increased turnouts in European elections and that ready access to advance polls before election day also increased voter turnout.
Second, the 2003 Pammett and LeDuc study I've referenced a number of times explained that the turnout decline in federal elections demonstrated that being too busy with work, school, and family was the reason 14.3% of the non-voting respondents gave to indicate why they didn't vote. There were other factors as well that can be covered by an advance poll.
The 1998 article “Voter Turnout at Federal General Elections in Canada”, by Louis Lavoie, makes the point that elections held on a day of rest can result in higher turnout.
There's a 2001 article called “Voter Participation in Canada: Is Canadian Democracy in Crisis?” by the Centre for Research and Information on Canada. In that one, they had a survey of the 2000 election; about 34% of respondents said they didn't vote because of work, illness, or travel, again things that can be solved by—