There is nothing we can do to make the design challenge less challenging or make the amount of work smaller. My tip is to look at what others do and learn from them.
I know Envato has different products.
.. and Zurb
From the jQuery website you can navigate to other libraries (in the top bar).
And of course the Stackexchange websites.
Just by the brief visits alone when collecting these links, I can already say unifying the header is done by all these examples. But by taking one step back you can see it's more about making components the same. The same shape, the same font, the same base colours, etc. The difference lies in the bolder accent colours. They gave every product it's own theme with it's own color scheme. The base colours are the same, like for example an offwhite color for the background, the same shade of black for the font, but different colours for the header, buttons and other links.
That is if you would want to unify the products, but still give the products their own unique identity.
I'm currently working for a company that has, well it's basically one product, but it has a bunch of modules that are basically different products. They all look the same, but only the content differs. That would be taking it to the extreme. But we were able to start from scratch and are with an team of 8.
If the task is forcing you to revamp the entire design of all the products there are some pointers I want to leave you with. I don't know what the products are you're talking about and how loyal your customers are, but people don't like change and big changes could scare them off.
Big changes could be unavoidable, but there are some things you can do to minimize any loss.
1. Small steps. Make small changes and ease people into it.
2. Preview the design. Make the new design optional. Offer it in beta stage and ask users if they would want to test it out. This is also great for testing. After official release, keep the new design optional for some time and force it on the left over users after some time. Do warn them ahead of time. This method is also great, because it makes people feel as if they are early adopters. It could make users more loyal.