I have found a very helpful entry in the Royal Gazette database - volume 34, pages 40 to 68 issued on April 29 1917. Innocently titled "ประกาศกระทรวงมหาดไทย เรื่อง เปลี่ยนชื่ออำเภอ" (Royal Order about rename of districts), this announcement not just list some name changes, but also includes all the districts which don't change their name at that time, thus it is a complete list of all the districts at that time. Sadly the monthon Krung Thep is missing, which at that time was under the control of the Ministry of Urban Affairs, and not the Interior Ministry as the others. But at least for some of the provinces abolished in 1932 I now know their territorial extend.
This announcement comes right at the end of the thesaphiban administrative reforms, as Prince Damrong resigned from his post as minister of Interior just two years earlier. With this announcement quite a lot of districts got renamed, some of the capital districts which were previously just named "Mueang" got the name of the province appended and thus already got the name they still have today. Other capital districts were renamed to have the same name as the subdistrict (tambon) which contains the district administration - which was also the main type of renamings done with this announcement. However in many cases the districts got back their historical name by the end of the 1930s.
Another thing covered by this announcement was the official change to use the term changwat (จังหวัด) for the provinces, which previously were still known as Mueang (เมือง).
I have converted the data of the announcement into a XML, which can be downloaded here. There are a few special cases where I am not fully sure about the identification of the district in the past with the modern-day one, but these are of course marked with comments within the file.