Hi Tom
This is a self-plug but will solve your problem for you, so I hope you don't mind. I have a product called Url Master which, amongst many other things, displays a correct 'http://mydomain' for the home page rather than displaying /home.aspx or, as you put it /lotsofgubbins.aspx.
While you can probably hack around with the solpartmenu and change the setting, you'll still get the problem popping up elsewhere, like in the logo skin control, the breadcrumbs skin control and anywhere else the Urls for the home page are automatically generated.
The Url Master module is a straight replacement for the standard DNN Friendly Url Provider, and handles all Url generation for your site. That way, wherever the Url for the home page is generated, you'll just get the site root value (note : you need to set the homepage in the 'site settings' page for this to work).
As a side bonus which your SEO guru will like, all of the old '/lotsofgubbins.aspx' urls can be automatically redirected back to the correct, shorter and more friendly urls so that any variations on your existing home page url (DNN actually has about 6 different urls that all point to the home page) will be redirected back to the site root Url. This also happens for any other pages already indexed with the 'old style' DNN urls.
There's lots of other SEO focused features as well, you can download a free trial version at http://www.ifinity.com.au/Products/Url_Master_DNN_SEO_Urls
regards
Bruce