Most local travel teams take a break during the LL regular season from about March until mid-June only playing in holiday weekend tournaments. There are a few that play through that period also. Around your area most of the teams play year around. That doesn't mean there aren't teams that don't welcome players who stop for football.
Your best bet is to check with some of the other parents of players from your LL all-star team. It is a good bet that a few of them are playing for travel teams. It is also pretty common for a manager from a local LL to put together a tournament team made up of kids from the LL all-star team and a few others.
Costs really depend on the team. We only charge for uniforms (~$50) and tournament entry fees typically about $35 per tournament. There are also travel/select teams in our area that charge $250/month/player from what I hear.
Check with other parents and check your local newspaper (not the LA Times) to find tryouts for travel teams in your area. You are in one of the strongest baseball areas in the country and there are a lot of teams in the area.
Here's a website that has some announcements on teams looking for players:
http://www.eteamz.com/baseball/announcements/index.cfm?bpage=1&startingrow=2004%2D01%2D09%2010%3A55%3A00