You're right...it's NOT exactly a Phillips although a Phillips will work.
Wentworth comes to mind, but I really don't think that was it. The difference between the Phillips and the unknown kind is that the unknown kind has barbs inside the common Phillips pattern that we know so well. It has grabbing surfaces every 45 degrees where Phillips only offers grabbing surfaces every 90 degrees.
In any case, I used an impact Phillips on mine, and there was no problem. The bolts came out easily.
On their death bed, nobody ever said, "Gee I wish I'd spent more time at work!"
'68 Sprite 1275
'76 Midget 1500