I think yours is a still-evolutionary one. The version I learnt in the mid-'80s was mostly improvisional, built around the same 4-line stanza with the 3rd & 4th lines repeated.
For the latter, I sung it in Tekong as "Hey-ho, AH! In-fan-try, AH! / Life is siong in In-fan-try, AH!" When I got posted to my Formation, we obviously changed it to "Artillery, AH!" though, with my unit's subsequent mono-intake, I taught my recruits to sing it as "B-M-T, AH!"
The opening 2 lines could be about any gripe, but always beginning with "Got no time to ..." & didn't necessarily have to rhyme. Usually sung during road marches, though we also sung it during 3-tonner rides (to keep all awake) & during the more-primitive Tekong booking out (lots of waiting around). Usually each peng took turns to come up with 2 lines & the others then echoed him, which could make for frequent giggles when the wit - or low-brow jibes - sunk in.
Really, the possibilities are limitless:
Got no time to brush my teeth, AH! (x2)
Got no time to wash my face, AH! (x2)
Hey-ho, AH! B-M-T, AH! (x2)
Life is siong in B-M-T-, AH! (x2)
Got no time to comb my hair, AH!
Got no time to kiwi boots, AH!
Got no time to go pang dio, AH!
Got no time to go pang sai, AH!
Got no time to go pang pui, AH!
Got no time to go pang pao, AH!
Got no time to masturbate, AH!
Got no time to pak chew cheng, AH!
Got no time to call daddy, AH!
Got no time to call mummy, AH!
Got no time to call honey, AH!
Got no time to call darling, AH!
Got no time to see movie, AH!
Got no time to go pak tor, AH!
Got no time to stand by bed, AH!
Got no time for first parade, AH!
Got no time to pack fullpack, AH!
Got no time to clean rifle, AH!
Got no time to take tea break, AH!
Got no time to eat night snack, AH!
Got no time to report sick, AH!
Got no time to take cover, AH!
& so on, lah.
