I've measured the spike before and without the power supply attached so I'm thinking that even though the circuit is handling things to a certain level it's just not enough and may eventually damage the op amps themselves by being continuously subjected to +60V at power on.
If I put this before the op amps and if f I have a VGS(th) of 3.5-5.5V such as with
this one, then at around 850ms or so this would turn on with the above circuit given the values of 100K and 100uF according to the calculation that I got
here. My settled voltage after rectification and filtering is 43.7V and is consistent between two separate power supplies. So, given that value, the 100K resistor, the 100uF cap, and the equation 43.7*(1-2.71828^(-85/100000*100)) I get 3.56V @ 849.7476ms. I made sure I verified the calculation and didn't just rely on the page itself to do it right so I'm confident in the values but I'm not sure how well it would work as I've never tried something like this before.
I don't have the mosfet I linked but I do have quite a few laying around to try this out with but am wondering if I'm just wasting my time with such a simple solution. Should I be looking into the app note above and calculating out a circuit for either figure 5a or 5b and trying that instead?