There is an old saying from Clausewitz: "Everything in war is simple, but the simplest thing is difficult." So there is a very simple solution to your problem, but you may have some difficulties with it. The basic concept is
simulate this circuit – Schematic created using CircuitLab
but of course God (or the Devil, depending on your source) is in the details.
First and foremost, the circuit is a lie, in that two FETs will not remotely do the job. I'd recommend about 20. This will allow 3 amps per FET, and assuming about 10 volts across the FETs, a power dissipation of 30 watts per FET. Both of these are perfectly reasonable mumbers for TO220 packaged FETs, and almost any n-type power FET will do.
Of course, if you did a quick bit of math in your head, you also realized that the total FET power dissipation will be in the 600 watt ballpark, so you're going to need a really hefty heat sink. This actually isn't all that hard or even all that expensive, particularly if you pay attention to forced air cooling - but you do have to pay attention.
Finally, that innocuous current sense resistor is going to cost you as well. 10 mohms at 60 A will give 0.6 volts, which explains the pot/resistor values, but it also implies 36 watts in the resistor. You'll want a non-inductive resistor for the job, and while they're available they're not cheap. Here's an example of what you might want, available from Digikey for 30 bucks and capable of handling 100 watts. With a proper heat sink, of course. Or you could simply run 10, 0.1 ohm, 10 watt resistors in parallel making sure to use a Kelvin connection. Again, managing heat will be something of a problem. And using a smaller resistor will reduce the heat, but an LM324 has 2-3 mV of offset, so you really don't want to go too much lower or you'll lose accuracy on your current set. Oh yes, and don't forget to take into account the resistance of your wiring. It doesn't take much at 60 amps to make a difference.
But it really does look simple, doesn't it?