(I still need to post a test with a black and white image...)
Before digital manipulation, you needed to do things by hand. Some blending modes could be reproduced in camera, some during develop or chemically and other could be reproduced in a photographic print and some more on a commercial print. Some others I am not sure that could be reproduced directly because they are using different channels to analyze pixel values.
I am not doing a rigorous approach on what calculations the blending mode does, but an "empiric" approach of the results. I am not sure in all cases because I have the feeling some blending modes are not using direct proportions but some kind of logarithmic progressions.
What are the pre-computer origins of these?
I am not sure that all have a pre-computer origin. On the contrary, a blending is in principle a way of computing color values. You could not do that before a "computer".
I can not cover all blending modes. But here I go with a couple.
The test image
This has some characteristics. It has a similar color of the one we are superimposing (r255g128b0) and some complementary one (blue jeans)
I also included a test band, with white, middle gray, black, the exact same orange we are using and the complementary blue.
Original photo: https://pixabay.com/es/lectura-libro-chica-estudio-515531/
Test Image http://otake.com.mx/Foros/Color/BlendingModes.jpg
The orange band
Using your example with an orange band:
This is the same as if you print a color photo and you print a band of transparent orange tint on the top of it. Take a look at this post: https://graphicdesign.stackexchange.com/questions/77703/preparing-design-for-duotone-printing/77708#77708 I use it to simulate a duotone. (Print)
Keep in mind that inks are transparent, so they mix of complementary colors still is transparent.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-01-Multiply.jpg
This could be as if you print on an absorbent orange paper. It also could be as if you put a strong color filter on your lens.
The difference is that the complementary color is neutralized to black.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-02-LinearBurn.jpg
The complementary color is not completely washed out, but the general result is this:
Instead of printing a grayscale photo with black ink you put orange ink. A monotone. (Commercial print)
Test Image http://otake.com.mx/Foros/Color/BlendingModes-03-Screen.jpg
Using a color gel, either as a filter on the lens or the source light.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-04-SoftLight.jpg
This could be duplicated with a duotone, but instead of black, you could use a (theorical) oversaturated version of the orange ink and a lighter version of the orange... yellow.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-05-HardLight.jpg
Something like an ortochromatic photo printed with silk print.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-06-HardMix.jpg
The result is similar to a duotone using black ink + the color. The amounts of color depends on how the complementary color is neutralized.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-07-Hue.jpg
A sepia photo was archived changing some silver crystals with other ones. In this case, the result is a change on the middle grays but leaving the shadows and hlights alone.
But if you use a color different from the orange you probably could not find a suitable crystal.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-08-Color.jpg
Using the same image
But the blending modes get more complicated when you use for example the same image. Then they could react as an overexposed slide or overexposed positive print.
Similar as the orange band, could be the same as printing several times on an inkjet printer the same image.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-11-Multiply.jpg
- Screen could be an over exposition. I am not sure but probably one full stop.
Test Image http://otake.com.mx/Foros/Color/BlendingModes-13-Screen.jpg
Pure brute force computation
- Diference is a total analitic blending mode, but could be at some extent a matt mask principle on a blue screen.