Firstly, horizontal take-off is not more efficient than vertical take-off. Wings only translate the energy you use in thrust into lift, and they translate it badly. Getting low altitude lateral velocity is a waste because all of that is lost in aerodynamic losses at low altitude.
Secondly the 'Cold Equations of Space Flight' article is absolute BS by a fool who doesn't know anything but NASA propaganda. For example, an LH2/LOX SSTO required mass fraction is actually .87, but only if your engines are altitude compensating (like SSMEs and aerospike engines are).
Thirdly, the biggest error in chemical SSTO designs is using LH2 as the sole fuel. LH2 has a terribly low density, which mandates very large fuel tanks and very large aerodynamic cross sections (thus adding lots of aerodynamic losses). Dunn has done a lot of good writing showing that denser fuels like UDMH, methylacetylene, and chilled propane are significantly superior fuels for an SSTO than LH2, to the point of putting as much as two and a half times more payload in orbit.
While the writer is right that air breathing to reduce oxygen load is a right direction to go in, doing so mandates spending lots of time in the 100k-200k altitude range, collecting air, incurring lots of aerodynamic losses. If you are using a low density fuel like LH2, you are wasting your time because the fuel has given your vehicle terrible aerodynamics.
There is an alternative. The RBCC (rocket-based combined cycle) engine that NASA has developed and all but cancelled (what is new, eh?) is the solution. This uses a rocket wrapped in a ram/scramjet and gives an average Isp of over 1500 secs. It needs to be dual-fuel: UDMH or Methylacetylene (welders MAPP gas is a suitable substitute) for the air breathing modes, LH2/LOX for the high altitude pure rocket mode. I'd also replace the LOX with liquid nitrogen. Yes, its not an oxidizer, but it is half the weight of LOX. As your vehicle is in air breathing mode, you bubble air up through the LN2. This liquifies oxygen in the air and evaporates the liquid nitrogen, so by the time you reach full rocket burning altitude, you have no more LN2, it is now a tank full of LOX.
LOX is normally 80% of a launchers gross lift off weight. Between this technique and the air breathing you can reduce this mass by 5/6ths. By using a denser fuel instead of LH2, you cut your vehicle mass empty by another 30-50% by reducing the tankage.
What does this mean? Lets assume you have a 1 million lb GLOW launcher burning LH2/LOX capable of putting 20,000 lb of useful payload in orbit. Using the above suggestions, you can reduce the vehicle GLOW to under 500,000 lb and automatically dropping the cost per lb to orbit by half.
Nor is, as is claimed by Chris Bell, an SSTO impossible. Putting six space shuttle main engines underneath a shuttle external tank is automatically an SSTO capable of putting 50,000+ lbs into orbit. Did you know a shuttle external tank only costs about a half a million dollars? If you put the six shuttle main engines in a recoverable pod, and left all the external tanks in orbit (to be collected for use in building a space station of proper size for the 21st century), since the engines are the only thing worth saving, you have a cheap to operate reusable SSTO. Carrying 1.6 million lbs of fuel at about $1/lb, you have a total launch cost of $2.15 million (versus the STS' $200-300 million), and a per lb consumables cost of $41/lb. Add in the cost of building and maintaining the engines and engine pods, facilities and launch fees, taxes and other overhead BS, and we are still talking only a few hundred bucks per lb.
Most of the insane $20k/lb cost of the shuttle system is in the 10,000 personnel that NASA employs to rebuild and reinspect every component of the STS for every flight (most of whom are union workers). Learning from the DC-X experience, as well as that of private companies like XCOR, whose EZ-Rocket is capable of multiple flights per day, we can trim assembly and launch staff to a few hundred at most.
Whether horizontal take off is technically "less efficient" than vertical takeoff I think is less important than the ground handling aspects of the two methods.
A winged vehicle with wheels can simply be rolled out to a runway for takeoff at any time. While a vertical launched rocket will require some kind of massive ground handling machinery, and much time and labor to carefully erect it on a launcher.
Those attendant costs of ground handling I believe would erase any efficiencies gained by vertical launches of a vehicle as you describe. Even using the 6 shuttle engines under a throw away tank requires retrieving the engine pod, refurbishing it and transporting it back to the launch point.
There are several "staged" methods of horizontal launch that I believe are also available to improve costs. Staging is expensive with rockets, because retrieval of lower stages is difficult or impossible, and vertical assembly is complex. While staging with winged horizontal aircraft I believe would be much less expensive.
There was a recent test of towing an F-106 into the air to simulate procedures where you could tow a vehicle to altitude to reduce fuel requirements. Also a vehicle was proposed that would use air-to-air refueling to tank with kerosene to power it to Mach 10-12 at 350k+ feet where it would release an upper stage from an internal bay.
Both of these ideas sound like airshow tricks. But they're very easy to do and require no blank-sheet-of-paper engineering. Gliders are towed into the air every day, and literally require a few seconds of ground hookup time. Air-to-air refueling is done daily by the military. Towing a ram/scramjet/rocket to Mach 3+ is very easy to imagine with an XB-70 class aircraft. I know where one of those is sitting in a museum right now.
These techniques aren't within the experience of the rocket men, so I think they're ignored when discussing the issue.
The other serious error is the requirement to boost very large payloads. Yes, very large payloads are occasionally required, and should be done with existing throw-away rocket technology. But small payloads, launched with minimal ground handling required, zero equipment thrown away, and launched almost daily will quickly amortize costs down within reason.
No matter what technique is used, until flights are flown with enough frequency to amortize the development and construction costs across many thousands of flights, then it won't ever be cheap enough for me to afford a flight. Fuel is cheap vs. development, hardware, and labor. Maximum turn arounds mean maximum amortization.