Like you, I've found a wide variety of fats in fudge recipes. To name a few;
The chocolate fudge recipe in The Joy of Cooking cookbook calls for both half-and-half and heavy cream. (From my home copy of that cookbook)
On this Macinac Island website, there's a recipe that uses a combination of whole milk and Crisco (vegetable shortening). http://www.mackinac-island-insider-tips.com/aunt-merrys-fudge-recipe.html
... and I found a recipe for Devonshire Clotted Cream Fudge that uses other ingredients I'm not familiar with such as golden syrup and castor sugar: http://www.food.com/recipe/devonshire-clotted-cream-fudge-238801
I think you may be obligated to experiment by making different kinds of fudge and discover your favorite homemade fudge. Sounds like a sweet adventure!
Fructose is one of the sugars in corn syrup. The problem is that 112 C is above the caramelization temperature of fructose, which is 110 C (230 F); this is uniquely low among the various common sugar molecules, most of which begin to caramelize around 160 C (320 F).
The toffee flavor that you are getting is due to the caramelization components.
However, without seeing your exact recipe it is hard to know what to change. I would suggest using table sugar with its much higher caramelization temperature instead of corn syrup would be the most appropriate solution.
It should dissolve the dairy, so you should not need to make a syrup.
However, sucrose (table sugar) has different crystallization properties than fructose and corn syrup, so after you get the main part of the candy mixture up to temperature and then cooled some, you might wish to add a tablespoon or two of corn syrup to help reduce the likelihood of graininess.
You could also try reducing the temperature to say 108 C, but this may affect the final ratio of water to sugar as less water will have been evaporated off, which would change the crystallization pattern in the confection, and thus is texture. It could end up quite sticky or even gooey.
It will probably be easier to search for a recipe for this confection that is already tuned to do what you want, as modifying candy recipes is very tricky; you must get the science and technique just right.
Note: fudge by its very nature is a a solid suspension of very tiny sugar crystals embedded in a dairy/syrup phase. The cooling and beating in traditional fudge recipes are to control the growth of the sugar crystals, so that they are numerous and very, very tiny (which gives the smooth silky texture) as opposed to larger and fewer (which gives a grainy texture).
As fructose and corn syrup tend to resist crystallization, it is odd to have a fudge like recipe with corn syrup as its main sugar component.
Best Answer
I'm not a professional fudger, but here is my theory: one should add it to the boiling mixture. The reason is that butter has milk solids that are said to “burn” at low temperatures (somewhere in the range 120C-150C or 250F-300F) which just above the soft ball stage (113C or 235F) needed for making fudge. I interpret the burning to mean that those milk solids (sugars and proteins) get a chance to contribute to the Maillard reaction that gives caramel (and its grained cousin the fudge) its great and rich flavor. Given how unique and varied the flavors arising from butter are, I would not want to miss their contribution by adding them after the heat is gone.