This isn't much help but I thought I'd share it with you anyway.
It's probably better to integrate your site into blogengine.
That's what I've done and it's worked out quite nicely. I used BE as a website framework and on any custom pages I inherit BlogEngine.Core.Web.Controls.BlogBasePage instead Page.
You could try to update the /themes/standard/site.master to match or inherit your existing master page?
I have been trying to create a custom page, inheriting the BlogBasepage, as you suggested, but am not having any luck. Would it be possible for you to post an example page code with .cs file showing how to do this?