Also, I need, but can't find yet an original strainer (I've asked evryone I can think of!). If I don't acquire one, I guess I'll need to just put another suitable vintage strainer? Below is a pic of the present strainer & also the one I need to get if it's to be legit.

I did a little research on this and based on Rob Cook's excellend book on Rogers here's what I found. Based on the lugs the era would be 1940's. On the badge you should be able to find the model as follows:

Soo Brand (entry level) Daisy Brand (better) Union Brand (better yet) or Three Star Brand (top line). I'll see if the book can give any help on the strainer.

Further stuff from Cook's book. Looks like your drum MAY be a Goodwill (Daisy Brand) drum. Finish would have either been Duco lacquer or Mahogany. The strainer looks like it may have been a Slingerland 3 point. They also used a Leedy strainer during that era but he only shows it on a brass shell drum. Maybe Rob or some other Rogers expert can comment on that. Nice find and I'm sure a cool old drum.

I'm judging from the imprint on the shell that the original strainer is the same as the leedy strainer in the pic above.

Here's the info I got from HarryC.:

That strainer is a Premier, made to look like a Leedy Presto?..I don?t have any, but if you find one or a drum with one on it, you will see ?Made in England? on the back..it?s a common mistake and misidentified in the Leedy book?Gretsch got heads from Rogers and sold/traded them parts..Gretsch got some parts and consoles from Premier?small world back then.