Methinks you will have no trouble with your iMac replacing the drive as the screen is held in magnetically. Get the right tools and follow and ifiixit.com description on the job. Consider buying a heat sensor kit from OWC as the fans will run full on if not used.
External cases are dirt cheap on eBay and such. Have you considered popping an SSD into a Thunderbolt external case and cloning the OS onto it and using it as the boot drive? You nwill get some 85-90% of the speed of an internal drive and then use the slow old internal for backups?