There is nothing weird about your idea. It is how most people go from smaller film to larger film for contact printing.
What you need is graphic arts film, A.K.A. litho film. You can get many sizes straight from Freestyle.
There are two main methods. Both involve the creation of an interpositive. The difference is that in method one, you create an interpositive of an intermediate size. Then you enlarge that interpositive with an enlarger to create your working-size negative for contact printing. The intermediately-sized interpositive is usually made on 4x5 film, since that it the largest size film that your average home enlarger will accept. In method two, you make your interpositive working size, and then contact print that to make your working contact negative. This may be necessary for those with tiny enlargers, and does not require you to buy two sizes of litho film, but it is supposedly not as sharp as doing the entire process via enlargement (i.e. projection). I have used both methods with fine results.
In one of the less-used methods, you process your in-camera film as a positive, eliminating the need for an interpositive.
You could also benefit by getting a handful of powdered chemicals to make your own continuous tone developer for the litho film. Litho film is designed for halftone results, meaning that you get either black or clear on the film, with no in-between tones. In lithographic work, the appearance of continuous tone is achieved by way of using tiny dots, not by having true continuous tone on the film. In one the film's purpose-made developers (the most common of which is "A+B"), this is what you get. However, continuous tone developers made for photographic work can pull continuous tone out of litho film. Some people use diluted Dektol. Some use diluted HC-110, Rodinal, or other photographic film developers. Others devise a combination of multiple developers, such as A+B, Dektol, and HC-110. IME, the most effective and controllable results, however, are achieved with a home-mixed developer called Soemarko's LC-1. I would get a copy of the Christopher James alternative processes book. He has a whole chapter on crafting negs for contact printing, and LC-1 is discussed there.
BTW, you will not need to "flash" the film. You will be able to print onto it almost exactly like you do with photo paper. One difference is that I always line the easel with a piece of black construction paper, to minimize fogging caused by reflection off of the easel. Another is that you will need a red safelight, as litho film is sensitive to yellow/OC.