I'm a swing trader, trading weekly and daily charts with about 50 trading events in a year. Expectancy: Around 0.68 Annual profit %: Around 30%. Sortino Ratio: Around 3 Worst Drawdown: Around 7%
Generally I think prop firms prefer shorter term traders, simply because they can look at your results over a week or two and get a general idea of how/what you're doing. If you're there 2 weeks and have 0-1 position open, especially if it's out of the money and you're telling them to give a week or two more to work out as you planned, well, I don't think they'll like that. I'm not saying it's impossible, just that I agree with your impression most are geared more toward short than long term.
True prop firms ( no capital contribution) look at the scalability and risk of your strategy then pedigree. These firms generally take on traders with Ivy league or other major college degrees eg Stanford, Cal, Duke, Colgate etc., swing trading will not be of issue I don't think because you can always trade around your core strategy. Prop firms that require capital contribution will take anyone that can clear U4, pass S7 or in some cases S56 ( though this may be going away) and have the minimum capital. The only other thing is that these firms have stair step commission structure and more shares/ contracts you trade on monthly basis lower the commission.
The simple answer to your question is, yes absolutely. To get a gig at a hedge fund you'll need a track record of 2-3+ years, on assets of 20+mm. Good luck!