I always back with TM but unfortunately enough for other reasons I disconnected it four weeks ago. Beware, evil is always watching, waiting! Lol!
The iMac went to the shop. The HD was bad. They could recover 100% of the User files. So happy.
Now, I'm waiting for a new 1Tb 3G SSD I ordered from OWC. I also ordered a new LG optical drive since factory one stop working 2 years ago.
Not really cheap but now I have iMac for another five years, I think.
Best
Eduardo
I can imagine you are afraid to loose some data. Always make a backup.
I think that your proposal is a good way to address the problem.
If it is a OSX-software problem you can simply connect your mac from an other system running OSX.
Your mac will then be treated as an external connected hard disk without using the (faulty) system that is on it.