Somewhat randomized thoughts and not any conclusions yet. Sort of talking to myself.
Your 4S Lipo will peak at 16.8 Volts, 14.8 is nominal. As long as the MB ballasts' input Voltage range is good up to 16.6 or so, the ballast will work ok.
Regardless of the input Voltage from your battery (again, assuming the ballast will handle 16.6V) then power output from the ballast to the bulb is going to be the same (also assuming that the arc gap, gas fill pressure and gas composition is the same). Ballast output should not change with changing input Voltage assuming the bulb specs are the same.
Is the power handling capability (Voltage range spec and Amperage range spec) of the non-MB Ushio the same as the MB-specific bulb?
"Only makes a spark in the lamp base". (The Anode/large, rear electrode end of the bulb?) Obviously, the bulb is not going to light off unless there is a spark across the gap. The purpose of the small wire (Trigger Wire) around the chamber is to ionize the Xenon during the ignition cycle and then the spark at the electrode ignites the ionized gas. Do you mean you see arcing between the bulbs' original base and the new adapters? Or is it arcing within the bulb chamber but well behind the electrode tip? Or is it arcing between the new adapter and the MBs' original contact? Have you tried to identify the location in a very dark environment (be very careful not to flash yourself if the bulb lights off)
Did you run the non-MB bulb in the momentary 75 Watt mode during the one run?
I have a loaner MB Clone. I used Parkers' adapters and the same non-MB Ushio bulb in this light with no issues and many, many starts.
Did you clean the bulb with hi-percentage alcohol and all the contact areas?
Does the original MB Ushio bulb still work ok?
On first blush, if you see arcing, then the ballast is PROBABLY OK (the ignition circuit, anyway). It seems like you might have a loose/electrically-poor contact issue or the power rating of the non-Ushio bulb is less than the MB-specific bulb and the non-MB bulb may have been damaged. Also, look closely at the metal ribbon connector material between the back end of the electrode and the bulb base for breaks. In you pic, there are wide/large ribbon connectors on MB-specific bulbs 1 & 2 but the connector looks very small on the non-MB bulb. (I realize there is distortion thru the quartz so I cannot really tell much on the bulb #3.) Also, the trigger wire on the MB-specific bulb is connected to the anode base and then runs down to, and wraps around the chamber. I cannot see any such connection on the non-specific bulb? Is there one? (There should be) If so, does it come from the Anode (large electrode) base?
The more I look at the pic, the more it looks like the Anode metal ribbon connector is gone and the small line that appears to be that ribbon connector, is actually the shadow of the Trigger wire?
