Mail, you didn't play a terrible game, you just made a really bad claim - or rather, a good claim that wasn't really thought through all the way.
Certainly from your perspective, what are the chances that we don't lynch you, but instead go on to lynch your actual Roleblocker? So your claim on the surface potentially sets your team up to find the Doctor. Great for you guys!
..... But with this particular setup it's a charade that you can't keep up. If you are the real Doctor, then the Auror dies that night (lock Doctor, kill Auror). So there was no reason at all for a Doctor to counter-claim you. The only thing you were doing is buying yourself a night to live. I had already claimed, so your roleblocker knew already that he could at least lock me down - I wasn't a threat. However, since claiming Doctor wasn't going to actually get your team any new information about PR's, there was nothing to gain by that claim. Had you claimed "Auror who didn't want to come out earlier when Galz claimed because you knew it would mean you get locked down by the scum Roleblocker", there's a good chance that people would believe you. I know a handful of people were absolutely itching for me to be scum fakeclaiming again. Yes, it means you die as soon as I flip - but a Goon for Auror trade off would have been GREAT for your team. And if it didn't work out... oh well. Letting yourself get lynched by not claiming is just as bad, and claiming Doctor didn't get you anything either.
So in your position, playing the sacrificial lamb isn't necessarily all that bad. But you've got to consider the returns on all your options. Claiming wasn't bad, and your play overall wasn't bad. I just don't think that you thought it all through. I think you made a snap decision that you would force out a Doctor Counter-Claim... without realizing that we had no need for one to come out. I think the other thing that you didn't really think about was the fact that for your actual roleblocker, healer was his only possible PR claim (He could claim VT of course, but we're likely to lynch anyway in that case). If he claims Auror, he goes counter to me and is dead (either via lynch, or House Vote). If he claims Vote Fixer, I think the real Vote Fixer would claim. That's a trade that's good for town (scum for Vote Fixer). So the only claim your Roleblocker could make that might buy him a day is Healer - since as shown, our real healer didn't need to counter-claim. This is primarily the reason that it was a good bet (albeit wrong) that if you were scum, you were the Roleblocker - a tell that you sent to not only town, but your scummates.
The fact that we DID end up flipping from you to Chairs is just bad luck for your team, and was generally out of your control.