You seem to have gotten a very nasty ST head. That much ratcheting of the output is as bad as I've seen, though I have see it in other waveforms sent to me after I made public my homebrew AVR design. Since you have so much excess capacity in the head, you might try adding about 60 uF of motor run capacitors across the output in hopes of smoothing it a bit. It is a crude solution that will cost you a bit in efficiency. I would try to return this head if possible...it's output is truly awful.
Adding capacitors to the rectified harmonic output sometimes (sometimes not) removes "harmonic hump" distortion. You don't have that as a primary issue, and so it makes no difference in the output waveform. It will do nothing for surge loads or anything else, except that it will boost the unregulated RMS voltage.
The quality of ST heads varies greatly, but yours is in the worst 10%. The stator laminated cores vary greatly, as well as the windings, wire used, and the quality of the case castings, etc. I recently had 3 ST-3 stators on my workbench- all different and varying by 1.5 inches in laminated core length. The latest replacements my neighbor bought from CGG (to replace a failed unit with aluminum windings on the rotor) had the harmonic winding so badly done that voltage was over 350 VAC. It could only be used with an AVR. The output waveform was however, quite good.
It's clear that the ST heads should be viewed with a great deal of suspicion. Resellers/importers often buy from the low bid source or the same source may have little or no quality control. The better built ones are still quite serviceable with replaced bearings and bridge diode. Ignore CGG's claim of having done these, my neighbor's ST-3 bearings were groaning within 20 hrs, and the "improved" bridge diode was junk. When you do get a unit with a very bad, ratcheting output, only replacement of the stator will correct it, and no one carries spares. I would insist on all windings guaranteed to be copper, and waveform without gross ratcheting, and harmonic regulation alone withing spec., with free replacement if found faulty. A dealer who actually inspected and tested his product (this is sadly NOT CGG) should be rewarded with a higher price.
I would suggest avoiding ST heads entirely except that there is no other 4 pole alternative withing a mile of price. In larger heads Gary of DES has recommended Stamford clones. For smaller heads (3-5KW it's tough and you're almost stuck with 2 pole heads like MeccAlt unless you are willing to play ST-roulette.
Best Wishes,
BruceM