I doubt a scale flying wing design could reach true Mach 1. You have to take the aerodynamics into consideration. Remember that when you scale down a design, you're also scaling up the relative speeds it will achieve (at 1/3 size, you achieve scale Mach 3 by the time you reach true Mach 1). So, you'll need a FAST design. The SR-71 still holds the world record for speeds attained by a jet. So, I'd say that it's a much better design option if you're not just looking to reach "scale Mach 1". So, make sure to factor scale into your equations and simulations, too, so you don't wind up just making something that goes fast, but nowhere near true Mach 1. Depending on just what scale size you use, you may keep running into the "nothing we've built can go that fast" wall, and have to design something even faster than the SR-71's design can handle (the real world limitation on the jet was skin temperature, rather than thrust and aerodynamics; It would be possible for one to actually punch the speed up enough to vaporize the titanium, if not for safeguards on the controls).
WHAT?! Since when does something SMALLER create MORE drag? That makes no sense. If that were REMOTELY true, I would have heard something about that by now, and I should know because I went to school for this.
You're also going to need a shitload of propulsion to pull it off. If you don't want to use a rocket, you're going to have to have a lot of fuel and powerful engines. Again, the SR-71 design comes into play. The body is mostly fuel tank and engines. Additionally, you'll need something like the nose cones on the engines to slow the air down enough to not cause engine flameouts near the Mach 1 barrier, while still providing enough oxygen for combustion.
Using a jet engine would be lighter, cheaper, and use a LOT LESS FUEL compared to a rocket. Here is why. Rocket and jets both use propellant to make something move. Now a ROCKET by definition has to have all of its propellant stored internally, and is usually the same chemical as the fuel for chemical rockets. A JET is air-breathing and therefore uses the AIR as the propellant and therefore ONLY needs to carry the fuel. That, and because it is far easier to cool for the same reason, the heaviest part of a rocket is usually the fuel/propellant tanks, and jets require far less fuel. This gives jets a far greater specific impulse (how long a pound of fuel can create one pound of thrust) usually resulting in a jet that create a fixed level of thrust for hours, and usually rocket that create the same level of thrust only for a few minutes, maybe worse.
Also, where you are may be a factor in getting jet fuel, it seems. Go buy some from Cheif or something. I know that if you tried getting some for a project like this around here, you'd probly wind up playing 20 Questions with the NSA... Of course, it doesn't help that this area is just plain too poor to support any population of people with private jets, so there're really no market for private jet fuel sales, here.
Again, I'm using ETHANOL. It should be relatively common to obtain since it is even used in gas-powered fireplaces. On top of that my most liberal estimates of fuel consumption is less than half of a gram per second.
