I would replace the cameras or refuse to do it.

1) Speco cameras (especially from that time period - 10yrs ago) were complete garbage. It is nothing short of a miracle all 8 cameras still work. Matter of fact, are you sure they all work? Are you sure they are Speco cams and several haven't been replaced already with something?

2) Any modern DVR with a large hard drive will do what you want. Any of them! From a cheap $200 unit from the flea market to a $10K unit.
Quality matters as always. So what is she willing to spend? Does she only want to spend $200? Then she will get a piece of crap. "But I don't want a piece of crap", then she has to spend more money - common sense.

I'm guessing this is not for a government building. So here is an example of something you could get for her: easy to use, descent quality, good price.
[Link: supercircuits.com]

Upgrade the hard drive to an 8TB WD purple and that should get you over 30 days with motion recording, when she has 16 cams. With only 8 cams, should get over 60 days, depending on the amount of traffic & settings.