You can download the Sierra installer whenever you need it. There is no limit to the number of times you can download - unless there is a data limitation from your internet provider. Apple has no such limit. I have downloaded Sierra at least a dozen separate times (don't ask why
), so I am sure you can download it when you need it.
Or, you can download by booting from your recovery system, and doing a reinstall of OS X.
Your EtreCheck took more than 30 minutes to complete. Most systems take less than 5 to 7 minutes. I think it mostly depends on the speed of the hard drive. (my SSD will run that in less the 2 minutes. even my older MacBook with hard drive, takes only 8 minutes.)
If the hard drive is original to your 7-year-old iMac, then I suspect the hard drive is slow, because it is near to failing. Looks like you keep a backup (good thing…), so the simple plan is to replace your hard drive, maybe upgrade to an SSD (which will take care of your speed problem single-handedly
)
Some of the red-letter entries in the EtreCheck file are of really old software. Those files can likely be removed from your system, as they probably don't work anyway….