gridplan, I do envy you, that is one fine bike. I believe I started a thread or talked a lot in a different thread about that bike when it was up for auction. Unfortunately, the search function is not working well right now. When it is better I will post the thread.
As for the age, in my mind there is no doubt, that is a prewar Gloria. The geometry, the Universal brakes, the non-use of chrome all says prewar. I especially love the fenders, oh so sweet.
As others know here, I am a pretty strict preservationalist, it is only original once. As soon as you repaint or re-nickel plate or change anything, the orginality is lost forever, never to be known again. Yes I am being mellow-dramatic but I tend to be somewhat alone with my views so I like to be a strong advocate of preservation. Here is an excellent article about automobile preservation,
http://www.nytimes.com/2007/08/19/au...in&oref=slogin
But, I will assume you want the bike functional and I can tell you finding parts form the 30s can be difficult at best. You can get the stuff, but you must have a lot of patience. If you can't wait, I would recommend keeping the original parts and ride with the replacements while you are acquiring the period correct parts. Your wood rims are a good example, I don't think I would want to ride on 70-year-old wood. (insert dirty joke here

)
As for the finish, tear the bike down, clean it (get rid of dirt and rust), repack with fresh grease and wax the paint, nickel and any bare areas on the frame and components. That should prevent any further corrosion. I understand this is your bike and we are in America and you have every right to paint flames on it, spread the back to put a 10-speed cog and have carbon wing-bars, but please don't. If it were mine, I would never consider new nickel, paint or anything unless it necessary for the function of the bike, e.g., it needs a new top tube, you should put paint on the new top tube.
One advantage to these very old bikes, the individual components back then were made for several years if not decades. Your chain is an excellent example. Originally it could have had a Regina GS (Gran Sport). Regina made those chains well into the 50s and I bought a NOS one not too long ago. Christophe old logo toe clips are another example. They made the same thing from the 30s to the 70s. Your question about the bar tape is another good example. The plastic is most definately period incorrect but it is easy to pick up Gaslo tape which would be period correct.
I have some questions if you don't mind. Are the brake levers cast aluminum? They look solid, not the typical bent aluminum sheet. Is the stem a steel Ambrosio? It looks like it from the picture but it is hard to tell. Also, are there other words stamped on the stem? What is the diameter of the handlebars? That can also solidify dating the bike. Is there a stamp on the toe clips and pedals? I would love to know who manufactured those. As a matter of fact, I would really love a list of the component manufacturers when you get the time.
I would be happy to help with any questions you may have as you work on the bike. Please don't hesitate to contact me.