Hmmm.......... I don't know whether I can be of much help at all here, since I'm strictly a seat-of-the-pants scratch cook, but gee, what an intriguing puzzle!
First, however: must you produce actual muffins from this mix, or will it be okay to use the mix to manufacture other goodies, just as long as you come up w/an edible result? If the answer is in the edible result category, then you're home and dry. AND about to have some fun!;)
(This is an aside) I seem to remember that a 12-muffin recipe makes a quantity of batter about equal to a 2-layer cake, so you can try baking a half-batch in your cake tin and see what happens . . . the main hazard I can think of is that muffin batter has to be stirred just enough to combine the ingredients; otherwise they come out tough and full of holes. So why not try the half recipe, per the package directions, and use your cake tin, and see what happens?
If you don't like the results--then make another half batch, only this time cut down on the liquid (probably by about half) so that you can spoon your batter out in blobs that won't run together; this should give you sort of spread-out muffins. (End of aside)
I think the hot setup would be to turn that muffin mix into biscuits (reduce liquid, pat out, cut out, bake), or cake (add sugar and another egg or so and some vanilla and/or some chocolate or cocoa, and then beat it smooth and bake like any other cake; or waffles (beat 3 egg yolks into the batter, beat the batter smooth, beat the 3 egg whites stiff and fold into batter - might need to add a tbsp or so of oil along w/the yolks just as an extra preventive against sticking); or banana bread (add bananas, a couple of eggs, flavoring, bake) etc etc etc . . .
As for the reasons behind all this.........the nature of muffin batter is such that leaving it unbeaten and confined within the muffin cups makes them peak in the center. Therefore it would seem logical to me that unconfined batter would behave altogether differently and would thus have to be experimented with.......
Oh, and I bet you could make a fabulous Yorkshire pudding in your cake tin! Just grease the tin, spoon in some of the juices off the roast, add the batter and bake .......... I've always wanted to try cooking a roast right on the oven rack with a pan on the shelf beneath, and then putting the Yorkshire pudding batter straight into the lower pan at the right time......... and one of these days, I am actually going to do it!!:D:)
Good luck, and let us all know what happens!