I did Plumbing and Heating for over 40 years.
Those valves are all interchangable, Shaw, White-Rogers, and Honeywell. But in your case I would stick with the Honeywell for ease of installation. Just write the numbers down and go to a reputable dealer, tell him your problem and he should be able to give you a replacement Honeywell valve. Look in the yellow pages and find the Honeywell dealer or supplier.
I'm partial to Honeywell myself, the White-Rogers, and Shaw seem to be more problematic for me.