I don't think it is the cable since your tests are all working correctly. My odds up front were on it being a problem with the COM port like a resource conflict. After watching your video I'm wondering if it is actually a problem with Windows 95.
Have you tried using straight DOS like 6.22 or something pre-Win95?
Have you tried making a PIF file for your EP software to run it under Win95?
If you haven't done either of those, I would start with the PIF file creation. Can't quite remember how to create one, but I think you make shortcut to the application and mess with the properties and it will allow you to do all sorts of limitations so that the DOS application doesn't know it is running under windows. Obviously booting directly to DOS would also negate the need for the PIF file. There is a PIF editor in the default windows install if I remember correctly.
Anyway, try those out... You have enough disk space where you are trying to save the HEX file? Just want to make sure you are not trying to save the file to a locked floppy or something like that. I agree with your sentiment that it looks like it should be working since you can dump the image and checksum the ROM. That's why I am suspecting a file problem. You might add some file handles in your config.sys if you have not done so already. Here is a link to Microsoft's site... This is for ME, but it talks about adding file handles to Config.sys for pre-windows apps and windows VM's once windows is running.
http://support.microsoft.com/kb/269030