Looking at the patent https://razors.page/patents/US1488907/ there are two spring extensions (part 40 - on the left-hand side of Fig. 2) at the back of the cap.
I can clearly see them in your video. Their task is to engage the back of the blade to move it firmly towards the blade stops.
I imagine you could ever so slightly bend those spring extensions towards the front of the razor.
This should put them into better contact with the back of the blade and maybe fix your problem.
You might want to try putting a bit of thick gaffer tape on the back of the spine of a modern blade to see if that fixes the problem.
If it does fix the problem, bend the spring extensions a tiny bit (one millimetre) at a time.
Anything you do to your razor is not my responsibility.
I can clearly see them in your video. Their task is to engage the back of the blade to move it firmly towards the blade stops.
Quote:...has spring extensions 40 within said cover or cap to engage the back edge of the razor blade when said cover or cap is moved to closed position, said spring extensions 40 serving to firmly bind the forward corner portions of the blade against the hooks 19 of the spring fingers 17
I imagine you could ever so slightly bend those spring extensions towards the front of the razor.
This should put them into better contact with the back of the blade and maybe fix your problem.
You might want to try putting a bit of thick gaffer tape on the back of the spine of a modern blade to see if that fixes the problem.
If it does fix the problem, bend the spring extensions a tiny bit (one millimetre) at a time.
Anything you do to your razor is not my responsibility.