Now I want to try what an inductor does.
10uH torroid ... not what I expected.
470uH - more what I expected, although it appears to only delay the steep portion of the rise.
4.7mH and it's much better.... longer / smoother / lower gradient.
What's the catch?
An apparent delay is a likely result of saturation: as current goes up, incremental inductance decreases, so dI/dt accelerates, and peak current moves from a gentler to more aggressive trajectory.
This can be exacerbated by ceramic capacitors, which saturate in an analogous way (ferromagnetic and ferroelectric materials have many similarities), with the difference that, since capacitance is reducing, the peak voltage Vpk ~ sqrt(L/C) * Ipk can be many times higher. (Which, since for an LC resonant circuit, normally this applies for the initial step, and you'd expect Ipk = Vin / sqrt(L/C), and Vpk = 2Vin.)
Wiring itself has inductance, within a geometric factor of the permeability of free space, 1.257 uH/m. Usually the geometric factor is less than 1, say 0.3-0.6. So 0.5 to 1uH per meter of cable length. Typical cabling is fractional to a couple uH, so you get time constants with ~10s uF in the low us range.
Damping is best introduced with capacitor ESR, and a good way to provide it is to put excess capacitance in parallel with the existing capacitor, and put the ESR there. Electrolytics are a good source of this.
Tim