Is the bradoon you want a loose-ring? If so, 5 3/4 would probably be just fine.
There is only the French link bradoon, the KK Ultra Soft and the Balkenhol bradoon (you could be riding with both Balkenhol and Bemelmans at the same time!!!) who come in 140mm in the HS bit collection.
From Neue Schule (only have loose-ring bradoon): you have the Starter (14mm), the Team up (12mm), the Verbindend (12mm) and the Tranz-angled lozenge (14mm) who comes in 5 1/2.
Stübben has a loose-ring bradoon (#2224 - 11 or 14mm)
What lenght is his snaffle right now? Do you have access to any 5 3/4 bit you could try on to see if the lenght could be correct?
Are you looking for a 10, 12, 14 or 16mm thickness for your bradoon?
What thickness for the weymouth?
(QUESTION : Is it brIdoon or brAdoon? FEI rules say bridoon while HS sprenger say bradoon…)