Before you start querying, you must, must, must familiarize yourself with submission guidelines - for the field in general, and for the specific agents and publishers you find are appropriate for you to query.
With this strategy, you're aiming to violate two common guidelines right off the bat. And even if your case, for whatever reason, is so exceptional that you think those guidelines don't apply, it's a safe bet that people considering your query will find these violations annoying and unprofessional, and be dead set against your submission from the start. Because, believe me, they get a lot of people who think they're exceptions.
Submit your manuscript, not illustrations
How to Find an Illustrator for your Picture Book says it all clearly and concisely. In a nutshell: you don't.
When you're submitting an MS for a picture book, do not submit illustrations unless you yourself are the illustrator. The article goes into this in detail, but the basic thrust is:
- Selecting an illustrator is the publisher's job, not the author's. The publisher will have a lot more experience, resources and selection than the author will.
- Publishers of children's books know how to read an unillustrated ms. That's what they do. I know it looks odd or sparse or incomplete. Nonetheless.
Do not call an agent
This advice is repeated over and over throughout the web. Janet Reid is really quite emphatic on the subject (also snarky).
Why is this? Moonrat touches on why cold-calling is so bad:
Don't call on the phone. Ever. Two reasons--1) The phone is bad for us, because we can't choose the timing. If you email us, we can address your issue thoughtfully and when we have time to. Plus the phone is super awkward--I always feel backed up against the wall when someone I'm not expecting to talk to is on the phone. 2) The phone is bad for you. If you get us on the phone and ask for the status and we didn't like it, we're going to have to reject it right there, on the phone with you. Also, maybe we were thinking "maybe" about your project, but now, since you've forced us to talk to you on the phone, we're suddenly thinking "no." Just. Don't. Call.
The other thing is that accepting open calls just makes agents and editors too exposed to too many people, some of them real weirdos (see Moonrat's full essay for more on that). So this is pretty much verboten, and it's not a line you want to toe.
Follow the Guidelines
I'm kind of dismayed that your reaction to hearing "publishers prefer X" is "well, I'll do X anyway." Well, if was just a preference ("We also prefer that your book be about vampires!), I could see that, but we're talking about an established industry standard. That's not the type of thing you want to mess with without an enormously good reason. Particularly as an unpublished author.
It sounds like you're not very familiar with industry standards, guidelines, and processes. I strongly recommend you get familiar with them before you start submitting anywhere. You've got a book you poured sweat and blood into, a book you're proud of, a book that's fantastic - you don't want to mess up querying, because that's just learning how these things are done, and then doing them.
My own advice is to find blogs by agents and editors, read them through, and learn what works and what doesn't. If there's something that seems to tick agents off, then really try to avoid doing that thing. I've found Janet Reid to be helpful, as well as the sadly-defunct (yet delightfully archived!) Editorial Ass (aka Moonrat) and Miss Snark. But in your case, I'd take special interest in children's publishing, which has quirks of its own. I don't have anything specific to recommend, but I'm sure you can find great stuff online. The first article I linked, on illustration, finishes off with some links that might be a big help for you.
Sorry to be discouraging, but I really hope this will be helpful. Better to do this right than to take a quick stab in the wrong direction. :)
