My first option would be to go the other direction: make the rental slightly longer than four days.
That's where I am now...using travel partners CDP and 924932, I'm able to get the "weekly" rate for ~$130 all in. My weekend rate (Thurs-Sun) had previously been ~$51 but I really can't stay in the area an extra day, so I'm just going to suck it up.
Thanks for your help everyone