This isn't exactly a splash screen (more of a preloader) but I found the following tutorials very helpful.
Here's the site where we use it, Fall For Greenville.
It took me forever to find something that would work (I know enough programming to be dangerous but couldn't find a full walkthrough) so I'm happy to answer any questions you have. In our example, instead of the .loading class that he mentions I put this:
Thanks for the information, Scott.
I needed something that stayed on the screen so residents could read some simple instructions to help them navigate the new map better. I can make something myself - I just was curious if anyone knew of a way within the JS API to do it.
Also, I really like your search widget. I don't think I've ever come across anyone else who uses that style over the traditional simple search widget. I might have to incorporate that into my maps...