I also posted this question on babynames.com. Over there 45 responders said they use "Soyer/Loyer", 12 said they use "Saw-yer/Law-yer" and one said she says "Saw-yer" for the first and "loy-er" for the second (she is from Indiana
11 of the 12 who use "aw" gave their places of origin. 1 just said "East Coast" of the USA; 1 was from Kansas, 1 from Oklahoma, and the rest from states in the Southern USA to the east of Texas. There may be a dividing line on this difference around the Baltimore/Washington area, as those from Baltimore seemed to say "oy" while those who grew up in Virginia
suburbs of Washington
, DC, seem to say "aw".
This was a fascinating question; thanks for posting it! :)