I asked the community hosts in this forum to contact the Apple Support team that is responsible for the Download pages with the updaters and they promised to report the problem with the GarageBand 6.0.5 download. But I have not heard of any result. And the current download is still the old version with the error message about "Invalid".
It is very difficult to get older versions of the applications for older systems, once the newer system versions are out. The advice I have given has been working until recently, and it has been the only option to install GarageBand on El Capitan. I have used it frequently. When I tested again, I am now getting the same message, when I try to run the GB 6.0.5 updater, even with the date set to the past.
GarageBand 6.0.5 would be running on your Mac, if you just could install the iLife version of GrageBand '11 and run the updater. Your Mac could also run an early version of GarageBand 10, but if the AppStore does not offer it for you to install, because the current version requires Sierra, there is no way outside the AppStore to obtain it any longer, unless a family member who owns GarageBand will help you by giving you a copy.
Try to contact Apple Support and ask for help to obtain an early version of GarageBand 10, compatible with El Capitan or a redeem code for GarageBand 6.0.5, so you can download it from the App Store.Sometimes Apple Support will help with older versions.