"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.

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.