The Wallace Wm's horns started at 001. The only reason I know this is I own number 19, and DJ used to have number 16 I think it was. As far a 1 per week I don't have any idea. On the later horns each model had its own serial number run. So you could see a 4, 5, 6, 7, 8, 9, or a 10 with the same number. Now I have also seen the same models with duplicate serial numbers. These were mostly model 1, 2, 3 from what I have seen. The model is stamped above the serial number. I don't know if theses also were like the older horns or all were consecutive. I have never seen a Wallace Wm's with a duplicate serial number,. or two different models with the same number. Koda I think it was had a 1055 and so did Dave Ashley. I have seen a couple of other like that too. But there are just not enough of the Wallace Wm's horns around to know.
To really measure the bore you would use a telescopic gage set. It expands inside the tube and then measure that with a caliper or micrometer. If you go to
www.use-enco.com and search for telescoping gage sets you will see what that is, if you don't know.
As far as "fixing the slide", I am unaware of anything in particular that is a recurring thing. These horns were very well made as you can see. If it made it this long in that good of shape it is OK! Be careful who you use to do the repair. A TIS horn is a lot more complicated than a modern horn. Because you now have 6 tubes to keep straight, not just 4. I would recommend John Upchurch or John Sandhagen. Both have experience with this style of horn. I don't know your location so you may have an excellent repair man there too. The gold plate also comes off very easily during repairs. Earl used for the most part King cases and a few from Olds. He worked for Olds in LA and Fullerton.
Also I see your spitvalve has been changed from the original. The original had a ball on the end of the rod. I will attach a couple of picture for you to check out.
One clue to age can be the hand grip. If it sez Patent applie/pending or has the patent number on it. The grip patent was applied for on Jan 4th 1928 and granted on Nov 25 1930. I have copies of all of Earls patents if you would like them I can email them as a .pdf file
If you would like more or different pictures of any of my horns let me know and I can email them to you
!