I can hook you up with good hat intel, but these lids are kinda pricey! Check out Miller Hats,
www.millerhats.com, and Peters Brothers Hats,
www.pbhats.com. I have 3 Miller hats, and they are all excellent, in my opinion. The one I wear most is a dark grey fedora of their Baldwin style. It has a teardrop crown, taller in front than back, which I just think looks the best, and about a 3" brim. For a Rorshach hat, you'd want a smaller brim so the crown appears taller. I'm a pretty good sized guy, so typically, I'd want a wider brim. I'd still wear a Rorshach lid, anyhow, even w/o being in the full getup, cos I'm a retro/film noir/pulp/nut.
I've actually contacted Peter Bros hats about making me a Rortshach number, & sent them movie stills, and a graphic novel picture as well of the guy. They'll custom make me one, but it'll cost $200 + $20 S&H. PB also custom makes Indy hats, western hats, and about any kind of lid you can dream up. Their stuff is primo, but you bloody well pay for it!
My Miller fedora more closely resembles one like The Spirit wears in the old comics. I do think, however, they probably have smaller brimmed ones that look alot like Rorshach's. A Miller fedora will run you between $90 & $130. They're good hats. I've beat the crap outta my fedora & it just keeps taking it! I've purposely worn it mowing lawns just to sweat in it & get it more broken in, it's survived multiple shaping attempts by idiots who, thankfully, didn't ruin it. It's survived some pretty ate up shapings by me before I did it right using steam from a tea kettle. I tweaked the crown shaping, front pinch (I prefer a tighter pinch), and bent the front of the brim down. I basically took what I remembered of some hats I saw some tough mugs wearing in old crime pictures on TCM and based my shaping on that. Worked out really well, too! I also did a way better job of shaping my $300 Resistol cowboy hat than any of the mopes in the western clothing stores did.
If you're looking for a swell, detective style, caped back, double breasted trench coat; I'd try Sierra Trading Post, London Fog, and even Ebay, believe it or not. I scored a sweet, tan coat from Sierra for about $60. I got a cherry, mint condition, black London Fog number off Ebay for about $65-70. Both were a steal! The Sierra one is my routine wear, almost "beater" coat. Like my fedora, it's treated somewhat callously at times, but it still looks great. Has a sweet, really warm zip out liner, too. The London Fog does, too.
As you can tell, I find this kind of thing fascinating, hence my rambling on & on. Miller Hats, & Peter Bros. Hats (if you've got the dough!). Good luck!