How to "fill" a cake made from a cupcake recipe
A syringe (or baster, but a syringe will be better) A LOT of holes, and frosting to hide the holes (though they will be pretty small if you use a syringe.)

Given the comment that  "I don't want it to be like several filled donuts joined together where it's not consistent" in combination with a refusal to consider layering it, you need 


a dense pattern of holes and 
a measured amount of filling in each hole.


So, for a 9x13 pan, you might be looking at 8x12 = 96 holes an inch apart, starting 1/2 inch from the edge, each filled with 1/96th of your total amount of filling. Adjust as needed for other size cakes and how well an inch apart suits your idea of "consistent" - you could go to 17x25 holes 1/2 inch apart and 1/4 inch from the edge, but it's going to be rather tedious.

Or you could TRY a more cake-centric approach - half the batter, the filling, half the batter, bake. It might fail miserably, it might "work" for some value of "work," it might require changing the filling to get a better value of "work." Certainly marble cakes and pudding cakes do things of this nature at the batter stage before baking.