This is one of those cases where I went down several dead ends and spent way too much time chasing after all kinds of reasonable, yet ineffective, approaches, only to collapse in a heap, look up, and see the solution, glimmering above me, all shiny and simple.

The problem at hand: Now that I've got a hold of a SharePoint list (SPList) object, and I also have the View I want to use to display this list (SPView), what are my options for rendering?

Stated more clearly: I have a particular View that is configured on the site that I want to use to drive which items, columns, and sort rules are used when I display my SPList. I want to do all this in a loosely-coupled way so that future changes to the site's view will be reflected in my rendered SPList. 

Dead End #1: Bind the SPList to a GridView. This is surprisingly ugly, though it does reveal a lot of details about what's going on under the hood of the SPListItems. Try it some time just for fun. It's educational, but not what you want.

Dead End #2: Attempt to create some other object that I can then bind to a GridView. How about a DataTable? Simple enough: build a bunch of columns, then populate the rows. Tried this, would have worked, but the effort to do so was a lot more steep than I'd expected, and it seemed like it would be error prone to continue going that route.

The shiny, simple, hindsight-is-20-20 solution: ahem...

myListObject.RenderAsHTML(myQuery);

d'oh.

Ok, here's what I ended up doing (roughly, my actual code is sprinkled across several methods, much of the error handling is removed for clarity):

// SPSite = site collection 

SPSite mySite = SPControl.GetContextSite(Context);

// You really need to set the following CatchAccessDeniedException = false setting! 

// In the event the current logged in user does not have access to the Web

//  (or any other resources) you are attempting to open later,

// this prevents SharePoint from automatically redirecting them to a

// "Authorization Required" page. Instead you will throw a catch-able exception

// which is not ideal as the answer to UserHasPermission() but it seems to be

// all we have.

mySite.CatchAccessDeniedException = false; // now we won't redirect on error

SPWeb myWeb = mySite.AllWebs["sitename"];

SPList myList =  myWeb.GetList(SPEncode.UrlEncodeAsUrl("/Lists/MyListName"));

SPView myFavoriteView = myWeb.GetViewFromUrl(SPEncode.UrlEncodeAsUrl("/Lists/MyListName/MyFavView.aspx"));

SPQuery query = new SPQuery(myFavoriteView);

Literal litOutputGoesHere = new Literal();

litOutputGoesHere.Text = myList.RenderAsHtml(query); // easy!