If the gun is as nice and tight as you say it is, then it should be mechanically sound. Hopefully. On a gun that has been refinished, the question of how hard it was rode comes to mind, but that may not always be the case.
The good thing though is parts are relatively cheap nowadays thanks to ebay, and the fact Jack First is making reproduction parts for all the old V spring action D/E/I frames. At one time parts may have been expensive, but the past few years have been cheap. I've amassed an amazing stash for pennies and dollars.
As to the serial numbers, I see mention of a "D" prefix in my bluebook pocket guide, and another member here. I don't think the actual guns got stamped with a D though, and this was merely done in the book to signify the universal short grip frame change. My '68 DS and the spare crane/cylinder a few thousand digits lower I have for it doesn't have a D stamped near the serial, and the OP didn't mention a D with his 914xxx range.
The only odd thing about the OPs is the later shrouded barrel and the finish. The short grip frame is correct for the '66 production date, and the hollow hammer pin is also correct for the '66-'68 time frame you usually see them on D frames. The barrel could be anyone's guess though. Maybe they returned it to Colt for a barrel issue and a new one got installed. Chances are it was changed when the finish was done, so not factory. As long as it was done right I wouldn't worry. My '68 is the old barrel and I have considered installing a shrouded just because, but I wanted to keep it original as it was on old LEO gun. So people do stuff just because. The overall condition is what matters, and since you only paid $370 it could be worse.
The only D frame I have been seeing locally for under $500 are REAL Cobras. They pop up in nice condition for around $400-$450. Detectives are usually asking $500-$700, but that's for that classic steel frame. It has been a few years since Detectives were under $500, probably since I bought mine for $325 and it's been awhile.
I forgot about the +P capability. I'm almost certain Colt never certified their D frames for +P until the advent of the shrouded barrel versions, so '73ish. With that was a servicing statement after so many rounds. However, the D frames prior to that, I wouldn't hesitate to load +P in anything '60s and later. Some might even go earlier than that, but I would never go pre-war2. I have shot +P in my '68 and even shot +P+ after some careful testing. Wouldn't do it all the time, but if one wanted to carry it for defense and maybe shoot on occasion to be familiar, it probably wouldn't hurt with a good condition gun. The older alloy Cobras are another story though.