I would interpret "go about on all fours" as meaning the creature in question
uses all its limbs to walk, belly to the ground. Is there any one who can
track that phrase back to hebrew?

I say this because, in modern times, WE have no complaints if someone says
"look, that person is down on all fours".
Nobody Ive ever met would correct him and say "No they arent, they are on
two arms and two legs, so you should say they are down on two by two."

I conclude that it is possible that the phrase "on all fours" is applicable
where 'all' limbs are being used to move, and the belly is toward the ground,
regardless of the number or type of actual limbs involved.
(Symbolising subserviance maybe? Kneeling an all fours? Like face-down praying?)