Thanks for the reply, @ciane. It was very helpful. I'm going to go for the more organized method you mentioned since I'd rather not have the hodge podge in the backup files. Luckily I haven't installed that much store content in the new computer yet so I am still hopefully able to figure out, like I did when copying and pasting the ebc files to my external hard drive, which gobbledygoop numbers go with which item by the time stamps on the stored ebc files.
I really miss my store items and old families and can't wait to get them back into my game. I just want to do it right because I already experienced store items uninstalling themselves on my old computer and hope to avoid that. There's a busy holiday season coming up. My sims will have turkeys to roast and gifts to wrap and all that decorating and I want them to be ready. :)