Yes, that's incorrect. What you downloaded was nothing more than the original firmware, patched to make it RPC1 [don't worry about what that is].
Check the thread posted by Les above. The first post in it has links to the Samsung Mini-FAQ & the older DVD-R lead-in issue thread. These will tell you what firmwares will actually fix it [other than the select TS-H652 firmwares].
Looking at the link you provided, is the TS-H652M Firmware Update (KC03) firmware the best one to use for this drive?
If so, now that I have the SH-182M firmware installed, is it correct that to change firmware to the TS-H652M KC03 I would have to use the -NOCHECK switch since my system now sees the drive as a SH-182M?
Yep. -NOCHECK is required.
This time, you might want to try to flash in Windows Safe Mode.
You might also want to try to extract the firmware .BIN file from the all-in-one firmware flasher you downloaded [if you haven't already extracted the firmware, then install something like 7-Zip or Universal Extractor, right click on the all-in-one file, and extract the contents to a folder] and flash using TSDNWIN: http://club.cdfreaks.com/2062183-post55.html . It might be less troublesome than SFDNWIN [if that's what's packaged with KC03].