If you have a log in for lip tat look-up on the jockey club website (I believe it’s free, at least I’ve had my login for like, 10-plus years and have never had to pay) you don’t have to have the full numbers there’s an area with a drop down menu to put in what you think the numbers are or leave a wildcard for a number you can’t quite read, I’d try checking colts and geldings and maybe also try leaving the letter as a wildcard though to my eye it definitely looks like Q with a very short tail. What year would “O” be, it could be that?
Just counted, O should probably be about 2 years older than Q so that’d be a 2011 foal and two years off wouldn’t be impossible by what you describe of his background?
It’s possible his jockey club name never changed, IIRC it’s pretty tough to change a TB’s name w/the Jockey Club once they’ve raced, offhand I don’t know the exact rules and it can be changed but there’s a lot of restrictions like they can’t have won a race, can’t be breeding stock, etc. and most OTTB owners if they don’t like the jockey club name won’t bother to change it and will just show the horse under whatever name they decide to call it. Send Noods, if he was ever called that, could well have just been his show name at some barn he was at after the track.
EDIT: Looking at the photo again, the way the spacing looks I almost wonder if the missing number, if he’s not an appendix QH or pure racing QH who looks really TB-like (I worked as security at a track, racing QHs regardless of how much TB is in the recent part of their pedigree don’t always look like regular ol’ backyard QHs. Some actually do but others not as much. And then some just look like really short TBs) is between the 1 and the 7 as the spacing looks uneven.
EDIT 2: Forgot to mention, just noticed it’s probably worth checking both bay and dk bay/brown for colors.