Trying to land an agent, as a mom of young children.

I have several picture books edited to my satisfaction, and I'm in the process of trying to find a Christian literary agent, but I'm a stay- at- home mom with a nursing baby, so attending conferences across the border is out of the question. Does anyone have any other suggestions for establishing credibility among agents and professionals? Is there any way to make contact, besides joining their slush piles, that doesn't come off as hard up, or creepy stalking? I've discovered that a lot can be learned from podcasts about craft and marketing, but no one sees the effort I'm putting in every day!

Also, how do you go about discovering relevant comp titles for a query letter/proposal to an agent? Do you have to purchase a software, or buy and read a lot of books until you get lucky and find one that's similar? I feel like I must be missing something, I'm hoping there's a method that's more efficient than just reading all the books.

Also, how long is typical to wait for a reply from a queried agent, especially from the Steve Laube agency? If a reply is favorable, is it more likely to come quickly? Does a longer wait typically mean bad news? How do you know whether you even need an agent? Has anyone successfully self- published a picture book? What about a series, all with the same characters? I have several completed manuscripts, and many more ideas, for my groundhog characters, the Happy Hogs. Would it hurt my chances of landing an agent later, if I self- publish the first book?

Thanks so much to anyone who can help me with even just one of my many questions! I'm very new to this world!