Here’s the problem you created for yourself: you have now set up an expectation with this client as to what level of work you do for what amount of money. Good luck raising your bid on the next one; they are gonna likely grind on you to keep working at the lower rate you established going in, even as the projects get more elaborate and creative.
Per-finished-minute rates that actually work out as a fair range for a particular project, do so ONLY by coincidence, IMO. NEVER use them.
Estimate the hours for doing all phases of a project, add up your costs, throw in profit and a slight fudge factor for unanticipated events, and from all that, generate an hourly and day rate that at least hits that minimum number that makes it all worth doing. You will use the figure to create a day rate and an overall estimate on the project you can live with.
Express the deal to the client as x amount of hours to a limit of Y amount hours, beyond which requires approving a new deal,and you are going to charge additional, and that you will discount X amount if you finish early. Typically, you structure the deal in thirds; one third (or however much you need to pay the rentals and assistants first) up front, one third when production wraps or you hit the first screeing of the edit, and the final third on completion and delivery of the finished dubs. This protects them and you: gives them control of costs and ability to kill the project without losing all the money, and it allows you to at least break even, should this ever occur.
The quote should express that they get one free round of change orders after viewing the first cut, taking x number of hours maximum, that they pay for additional changes after this, plus fixing things that are their fault, like them giving you somebody’s name or title wrong, and that you eat the cost of fixing what YOU do wrong, like typos you made in the CG when they gave you the right spelling. Establish up front if this is a work for hire or not, and who owns the finished master and source tapes. These will eliminate the bulk of problem areas for such productions.
You might consider adding a clause that holds you harmless for legal probs and puts the onus on them to get any legal clearances taken care of for things like music rights.
All of THAT will get you more in the ballpark, and getting paid more than the fry cook at McDonald’s. Charging a per-finished-minute fee, you might find yourself actually LOSING money on the videos over doing something else like cooking those fries. That’s not a sustainable business model.