keep in mind that it is very important that I am familiar with Wordpress. My partner is also familiar with it, and he knows even less about computers and programming than I do.
You may be familiar with a hammer but that doesn't mean you use it to take apart an engine
And, really, I don't understand why you say wordpress can't do this.
Not saying it can't do this, saying the way your spec is worded is not how Wordpress "puts things together". Quickly looking at nextgen gallery and it looks like it styles posts and adds widgets.
You can see this by their demo:
It works within the post "space". This goes to my bullet points of what your options are.
Please don't take any of this in a negative way even though it's how it comes across. I'm truly trying to help you so you don't waste money.
this may work for you: http://gallery.menalto.com/ (free and supports videos)