In this case, I didn't have a "mismatch", but rather a "Missing" profile. Maybe I should be saving the scan to Adobe RGB, then converting to ProPhoto. I usually don't add a profile in the scanning software - I'll give that a try.
When you scan the scanner should be scanning into a defined RGB space. This should be selectable with your software. I don't understand why no profile is embedded. Check your scanner settings to make sure colour management is set up properly.
If you want to work in ProPhotoRGB in Photoshop, don't scan into AdobeRGB. Taking a "clipped" image then putting it into a bigger colour space won't be as useful as scanning into as wide a gamut space as you can first. If you don't have ProPhoto as an option in your scanner software try something like WideGamutRGB.
I am not a colour expert, but I recall that for scanning film, some pros prefer specialized spaces like Ektaspace or ChromeSpace 100 (both by Joseph Holmes, I think). Perhaps a real color expert like Andrew Rodney will offer some advice on this.
The way I see it is that there are more advantages to being in a bigger space than a smaller one, as long as you are using 16 bit/channel, and this is important. ProPhoto can store any color that we can capture or see but because it is so big you don't want to break each channel into 8 bits of resolution, you need 15/16 bits.