"securely transmitted to a third-party vendor for billing under strict privacy protections" doesn't exactly calm my paranoia, though. It seems like any company gets its customer database compromised, sooner or later. I would probably opt for the "all you can drive" option.
reason.org
"A common concern about mileage-based user fees is privacy. Many people are uncomfortable with the idea of disclosing to the government how much and where they drive. But there are ways to manage these concerns. Mileage-based user fee programs should allow drivers to choose which method of assessing their fees they feel most comfortable with, as they have been doing in pilot projects in about a dozen states."
"One option would be to simply report annual odometer readings at the time of vehicle registration renewal. Another could be an “all you can drive” option, which would have users pay a higher than average fee in exchange for keeping their actual mileage private. Drivers desiring the most accurate assessment of their driving fees could install a unit in their vehicle that records miles driven or use GPS to log which roads they used. Even with these options, the government need not possess this data: It could be securely transmitted to a third-party vendor for billing under strict privacy protections. This has proved popular in pilot projects conducted in other states. "
"A critical element of using mileage-based user fees is that they would replace the gas tax, and not simply be assessed on top of gas taxes. That’s why in our report, “How to Replace Michigan’s Gas Tax with Mileage-Based User Fees,” we recommend the state reimburse or credit drivers for gas taxes they might still pay when driving on a highway that has been converted to mileage-based user fees."

Why Michigan should replace gas taxes with mileage-based user fees - Reason Foundation
State policymakers should start thinking about a permanent replacement for the gas tax, such as mileage-based user fees.

"A common concern about mileage-based user fees is privacy. Many people are uncomfortable with the idea of disclosing to the government how much and where they drive. But there are ways to manage these concerns. Mileage-based user fee programs should allow drivers to choose which method of assessing their fees they feel most comfortable with, as they have been doing in pilot projects in about a dozen states."
"One option would be to simply report annual odometer readings at the time of vehicle registration renewal. Another could be an “all you can drive” option, which would have users pay a higher than average fee in exchange for keeping their actual mileage private. Drivers desiring the most accurate assessment of their driving fees could install a unit in their vehicle that records miles driven or use GPS to log which roads they used. Even with these options, the government need not possess this data: It could be securely transmitted to a third-party vendor for billing under strict privacy protections. This has proved popular in pilot projects conducted in other states. "
"A critical element of using mileage-based user fees is that they would replace the gas tax, and not simply be assessed on top of gas taxes. That’s why in our report, “How to Replace Michigan’s Gas Tax with Mileage-Based User Fees,” we recommend the state reimburse or credit drivers for gas taxes they might still pay when driving on a highway that has been converted to mileage-based user fees."