You can advertise in any number of music trades like Billboard or contact organizations that deal with music industry employment (NARIP, for one) to find someone to handle your publishing catalog (if you’re willing to pay a salary). Publishing administrators wear many hats, from trying to place music to collecting money to making sure the paperwork is up to date. Administrators find money in anything that uses music like film, TV, advertising, web sites, etc.
Obviously, the best arrangement is for the person who writes the songs to have it clearly stated that they wrote the songs. Consult an attorney with specific knowledge about intellectual property. You need to get a clear agreement as to who owns what.
Hopefully you are signed up with a performing rights organization like BMI (see Is a Performing Rights Organization the Same Thing as a Publisher?. PROs collect money from radio stations (and other businesses that use music) and distribute them as royalties to songwriters. You can only get paid from radio play if you are affiliated with a PRO.
Home recording is so inexpensive to do that it shouldn’t be an obstacle for anyone. A nice home studio can be set up for under $1,000. You also might be able to work something out with a local recording studio, which are often in need of business since the home recording revolution took hold.
There’s no one perfect answer, but you have to get the attention of the person who’s booking the festival/tour. Show them that you’re drawing big crowds at your gigs and that you’re getting a lot of radio/retail/press attention…you get the picture. State your case in terms that translate to people showing up to see the show.
You should sign with a manager when the opportunities a manager can create are better than the ones you can create yourself. Or if you are spending more time deal making than writing songs, you should get a manager. A good manager can drum up new business, coordinate your existing business activities, and generally advise you and propel your career forward. Managers get a percentage of your earnings, so your ideal candidate (a) believes in your career and its possibilities, (b) is aggressive in seeking out new revenue streams, (c) is looking out for your long-term best interests in any deals that are made and (d) is trustworthy.