I had to look up what is this "ultrasonic" ignitor. Read the description on the manufacturer website, and all i can say it describes exactly a standard superimposed ignitor, like what's installed in 90% of ordinary HPS street lighting throughout Europe, but for 3x the price
For a probe start ballast with Voc around 240V (probably will be ok up to 270..300V), Get a Vossloh Schwabe Z400M, Bag Turgi MZN400, or something similar
https://www.ebay.com/itm/316160991645Momentarily shorting a HID ballast - I expect this be ok for the ballast, as the ballast is made to withstand momentary dips in the arc voltage of a cold lamp. However it may not be effective for starting a lamp. As matter of fact i tried to light an HPS this way, shorting the ballast output 30 times, and have not started the lamp. Maybe i would have better success with a MH lamp, but i have not tested it
Other question - Is the current spec of the ballasts compatible ? I thought your Pulse Start ballasts follow what we call HPS specs (250W lamp 3.0A arc), while Probe Start what we call Mercury specs (250W lamp 2.13A arc) ?