Yeah, probably the best survival strategy would have been investigate Persus13 N2, and then claim it immediately D3 while calling for a mass-claim.
Mass claim is generally the best shot town has when down to 1 dopp, and usually happens, so by being very pro-town and upfront about it as scum you give yourself some cover to try and buy time to win.
I'm not sure you could have won given the situation, but you certainly could have gotten at least to day 4 and maybe 5 before you got lynched by some clever use of the knowledge you have. Especially since, once the town starts full claiming, it's easier to just lie as a dopp detective and say stuff like 'Yeah, I checked so-and-so and they are what they claim' when you actually did a kill.
I donno, I did do exactly that. With Caz. With Tric. Didn't work. Not even D4.
The issue here wasn't that you tried to do exactly that, it's that you tried to do that
after everyone else had already been doing a mass-claim but before you volunteered your info. If you had been an early part of the mass-claim with actual new info you'd have seemed town.
Once the mass claim is over, no one expects the Detective to have new info other than to attempt to catch scum in a lie. Which is why you can lie about what you do while actually killing people.
But by waiting to say that you're a detective until after everyone else had already claimed, you gave up your chance to show that you're pro-town and looked more like a dopp that had failed the kill instead of someone who legitimately did an investigation.
I get that reading is slow for you and can miss stuff. That makes this harder, for sure. I'd recommend keeping a notepad or spreadsheet with the players and what roles they claim or have others report that they have. Including stuff like a sneak or reporting saying that so-and-so left their house or visited x. This is both a good practice in general, but it also means you can focus your skimming on that information first. It's critical to know, both for town and scum, and is the type of stuff that can come back and bite you if you miss it.