The Haucks were total custom rifles, what you ordered was what you got and paid for - $300 when a Winchester Model 70 Supergrade was $185.
I found another reference to the Hauck in 'Rifles, a Modern Encyclopedia' by Henry J. Stebbins, 1958. You can find this one at gun show booksellers every now and then. A few quotes:
"For some years he has been making his own, a hammerless falling block lever action with flowing lines that rather suggest the Savage 99 receiver. It has a speed lock, with only 3/8" hammer fall, and both hammer and firing pin are retracted before the breechblock starts to go down...
In other ways this entirely modern action is built to handle modern ammunition, practically everything from .222 Remington to .375 H&H Magnum...
The rifle shoots high intensity cartridges with accuracy, the barrel shank that enters the receiver is long and thus adds to the stiffness of assembly. So does the bolt that binds the stock to the receiver. Finally the forestock is floating, it's attached to a metal hanger that is screwed into the receiver...
The Hauck single shot is well adapted for use with rimless cases, when so ordered. Few others pull much reloaded and unresized brass of this type reliably, but this rifle has to be modern and is."
Sounds a lot like a Ruger No 1, doesn't it? About 25 years early.
Note that this is about the Hauck made guns. I have not seen anything at all about Matteson and have no idea how closely he followed the Hauck design or quality. You have that one to look at. Maybe a real expert will come along.