I'm 99.9 % certain it's a model 1908,but I was wrong a week or so ago about something and my confidence in knowing it all is severely shaken
Now as for this:
"If they sold it as a Colt, model 1903 and I bought it as a Colt, model 1903, what do I put in my bound book? model 1908?"
That's is one of those many shades of gray areas the ATF is well known for.
My guess would be to correctly ID it in your book with a footnote about the previous mismarked model number.The serial number being correct is a bigger deal to most fed's anyway.
This isn't as big a nightmare as the new gun a dealer got with the wrong serial number recorded from the box,not the gun.I don't recall what Wally had to do about that,but I'm sure it had to sit in the safe until it was straightened out.
Hope this helps,Robert.