Makes sense. I honestly didn't think of the different architectures. I was thinking virtual machine meant virtual machine, but I guess the keyword really is "virtual." Plus, it didn't dawn on me until long after I made the post, but I have one Pi 3 and one Pi 4, so it still probably wouldn't be a straight-up copy/paste/dd operation, anyway.
In the end, I just did it the old fashioned way, but used one of the remote-control apps on an Android tablet. Then I could use the browser to find links and stuff, and didn't have to type things out with my remote in the on-screen keyboard.
Thanks for the input.