So let's say I used the ICM Epson sRGB setting. What happens? Does the scanner embed the sRGB seting in the file? If so, how would I use this or can;t I in Lightroom or Elements?
Yes, the software Epson Scan embeds the profile „Epson sRGB“ into the saved file. But as this is a general profile, it won‘t be of much use.
As it seems that you want to stick with Epson Scan, I‘d recommand setting „Configuration...“ to „No color correction“, thus producing flat TIF-files, opening those in Lightroom and doing all corrections there.
Here's an idea I just thought of. What if I adjusted the flat scan of the transparency I got from X-rite so that the results on my calibrated monitor matches closely to the transparency illuminated by a 5000K LED back light panel. Could I apply the same manual adjustments then to any scan to approximate proper colors? In doesn;t seem likely since every chrome is different.
Why not doing it visually, as with Epson Scan (and without Photoshop) I don't see how to get a more colorimetrical correct result. Later you can define presets in Lightroom as soon as you found out what corrections need to be made for different scans (E6 film types, flatbed,...). Starting with the x-rite target as your first scan is ok, but you will make your final judgements on real world images, so I would not spend too much time trying to hit it perfectly.
But then how does an ICC profile work in PS? It also doesn;t know what the original shot looked like.
If you want to steal a glance at a copy of „Real World Colormanagement“, this drastically increases one‘s understanding of ICC profiles etc. Recommended reading.