As an automotive tech (ase master + L1 + L3 blah blah) it blows my mind that this type of PTO engagement even exists..
On car we call that a 'clutch dump'. Or, if it's a multiplate wet clutch like an auto trans, we call it a 'neutral drop'.
And both are classic recipes for broken axles (ie shafts) among other things. Other than the foot pedal clutch on a manual transmission, every other type of clutch engagement on anything modern is usually 'pulse width modulated' which means rapidly switched on and off in a way that simulates releasing a clutch pedal properly. To me, it's sheer laziness that this isn't SOP on tractors with electric pto switches. I get why it's not a thing on riding mowers (to my knowledge?) because of the price point, but on tractors it just seems.. lazy!
Unfortunately that type of control is not something you can 'easily' implement because even if you built the control circuit to do it, you'd have to 'tune it' to function properly. A lot of work unless you're into electronics and enjoy that kind of thing. If it's a regular old electromagnetic dry plate clutch like a big version of what's on a riding mower, depending on how much current it flows you might be able to fairly easily rig up a lower voltage 'starting circuit' with a large resistor of some kind (coil ballast resistor or blower motor resistor pack are cheap car parts which could be made to work) and a timer circuit. It would start the clutch with the resistor in series, and then bypass it after a second or so. But would still require fiddling to find the right resistance. Or, a large capacitor in series with a resistor (both values would require experimentation). If you ARE working with a multiplate wet clutch or a band clutch applied by a servo you could install a variable restrictor into the flow path and mess with it until you like how it works. I used to rebuild automatic transmissions and this is anologous to a DIY 'shift kit'. Doable but requiring a lot of background knowledge and a major time/effort commitment to get working properly.
A slip clutch adjustment would be the easiest 'bandaid' if you already had a slip clutch. Other than that, no real EASY way forward.. sadly. Sucks that they even build them this way to begin with, in my opinion.