If you check back on this thread, I've posted audio of how I say it. I think it's 'cross' that's really different - US doesn't really have that short o sound but has an 'aw' instead. If I say 'criss craws applesauce' then the intended rhyme makes itself clear.

"Cross" is very short in British English dialects, meanwhile "sauce" is much closer to "source", to the point that they're almost indistinguishable. American English dialects tend to elongate the "ahh" sounds.

Sauce: I used to speak in American, but now I speak in bastardised English where I trip off the path and whipe my ass on the grass, but no one ever knows how I might pronounce those words.