Hi, I'm the author of the iFinity Url Master module you mentioned. With this module, you can achieve what you would like to do. You can create 301 redirects from the .htm urls for your existing html files over to the equivalent DNN pages, and you can replace them page by page so that at one point it serves up a .html page, and at another point it starts serving up the DNN pages.
I have done what you wish to do several times, for sites based in old asp (.asp), php sites (.php) and plain old html sites (.htm/.html). It's pretty easy to do, just requires some planning.
However, unless you have thousands of pages I would just copy all the content over at once, and launch the new site altogether. It will be quite difficult to get a cohesive look in your mixed old/new site, and getting all of the links to work together will be troublesome.
My recommendation would be to go through and work out your existing sitemap,ie
index.html
products/widgeta.html
products/widgetb.html
etc...
and then create the equivalent dnn pages (home, products. products/widgeta, products/widgetb, etc...
Copying the html from the html pages to the DNN pages should be a relatively simple copy/paste operation into the fck editor in DNN.
Once you have done this, you can set up the custom 301 redirects so that all the external links for your old pages will refer to your new pages.
Doing it in a 'big bang' approach will cause less problems in the long run, as you will spend a lot of time fiddling around trying to get menu systems, etc, to tie in together.
For your reference, this forum post explains how to redirect .html pages to the DNN .aspx equivalent using Url Master: 301 Redirect .html to DNN .aspx pages
I hope this helps, feel free to contact me if you have further questions.