Would a 120/240 V whole house surge protector work with 120 V single phase?
I have done exactly that in a similar situation. It did not explode or anything.  The unit I used was a HEPD80 from Schneider.



I capped one of its hots and wired its remaining hot, neutral, and ground in parallel with an L5-30 plug and receptacle to improvise "an L5-30 surge protector" which otherwise does not exist or I couldn't find one.

I have no proof that it suppresses surges.  But it seems not to have contributed negatively.  I could not imagine any way it would hurt.

As expected, only one of the "OK" leds light up.  That could be confusing for future residents, so you might want to label it appropriately.