The op-amp idea was one I had thought of and discounted as they don't always provide a lot of current. Looking at it, the LM339 can't sink a lot of current (max 16mA) which might be a problem. An LM324 can do about 20mA sink, 40mA source, though not sure that's enough either, especially if we want fast turn-off times (see below). They're also fairly slew limited, which would be an issue.
Even if we did look at an op-amp, an LM339/324 can take 30VDC, I don't really recommend putting it on one of the voltage rails. Apart from the fact that we've got 3 of them (and they won't all necessarily be the same voltage), the gates on the IRLB8743's only take 20V max (from memory). Running it or a driver from the rail that runs VIN is a better choice.
I'd also considered replacing the 12V reg with a 9V reg (7809). This still gives a reasonable voltage for gate drive (much further up the drive elbow than 5V), and is more than adequate for running the Arduino (taking even more voltage drop away from the Arduino regulator under the shield, and thereby reducing heat generation under there - which could eventually be a problem). It also removes the need for the 12/24V jumper, as it'll always be on regardless. It'll require a heatsink if you run it off 24V, but the same was true for the 12V reg. Also, this gives a 3V margin at 12V, so the reg will run reliably (if not, we can always use a 7808 to get an extra volt overhead, at the expense of drive voltage).
Also, we do want (reasonably) fast turn-on times, but we can live with slower turn-off times by adding in a diode reverse biased across the gate drive resistor (anode to the gate, cathode to the drive). When the drive output goes to ground, this gives the gate a higher current back-path, effectively taking the gate resistor out of the loop till the gate is at the diodes forward bias voltage (eg: 0.6v). For even faster switch-off without going to a full gate drive, you can use a PNP switch-off transistor & a diode. This removes the current sink issue, at the expense of dropping the gate voltage by the diode's forward bias value (eg: 0.6v).
FWIW: The biggest issue with drivers is usually the amount of components that have to go around them, I know this isn't always the case, so please remember to take that into account when mentioning costs and usage. It also affects board real-estate.
Even if we did look at an op-amp, an LM339/324 can take 30VDC, I don't really recommend putting it on one of the voltage rails. Apart from the fact that we've got 3 of them (and they won't all necessarily be the same voltage), the gates on the IRLB8743's only take 20V max (from memory). Running it or a driver from the rail that runs VIN is a better choice.
I'd also considered replacing the 12V reg with a 9V reg (7809). This still gives a reasonable voltage for gate drive (much further up the drive elbow than 5V), and is more than adequate for running the Arduino (taking even more voltage drop away from the Arduino regulator under the shield, and thereby reducing heat generation under there - which could eventually be a problem). It also removes the need for the 12/24V jumper, as it'll always be on regardless. It'll require a heatsink if you run it off 24V, but the same was true for the 12V reg. Also, this gives a 3V margin at 12V, so the reg will run reliably (if not, we can always use a 7808 to get an extra volt overhead, at the expense of drive voltage).
Also, we do want (reasonably) fast turn-on times, but we can live with slower turn-off times by adding in a diode reverse biased across the gate drive resistor (anode to the gate, cathode to the drive). When the drive output goes to ground, this gives the gate a higher current back-path, effectively taking the gate resistor out of the loop till the gate is at the diodes forward bias voltage (eg: 0.6v). For even faster switch-off without going to a full gate drive, you can use a PNP switch-off transistor & a diode. This removes the current sink issue, at the expense of dropping the gate voltage by the diode's forward bias value (eg: 0.6v).
FWIW: The biggest issue with drivers is usually the amount of components that have to go around them, I know this isn't always the case, so please remember to take that into account when mentioning costs and usage. It also affects board real-estate.