Was thinking about this and other ways to allow bereft teams to still be competitive. What about instead of an insurance system, an alternate player system? Each week, randomly select a number of players equal to the number of owners. Use an online dice roller or something to help with selection. Allow these players to be the "backup players".
Following the order of weakest team to strongest team, let owners select an extra player from the backup player pool. That owner then gets the points that player produces that week. They don't own them, so this takes nothing away from actual owners, and since everyone is allowed to participate, the teams that are doing well can't complain as they get extra points as well. It also keeps the gambling and payoff risk involved in the competition, along with research and matchups, etc. It is, however, more work than your insurance idea, depending on where/how you planned on establishing your player averages.
For an example, as a commish of a 14 team league, our third week randomly generated backup player pool could look like the following list. I used a d20 to select the QBs, a d30 on RBs, a d40 on WRs, and a d10 on the TEs.
There are a few issues, of course. A commish would have to draw and post this by Tuesday morning and the owners would have to make their selections by Saturday. You would need to have every owner post their pick publicly and quickly, or have each owner reply with their preferences in an ordered list and then hand out the players accordingly. An easier way to do that would be having far less players (4-6), each one only selectable [x] amount of times, then having the owners rank their preferences with you handing out the results.
Definitely needs work but could be an idea.