"If escape velocity from Earth is ~ 11.3 km/sec, then an impetus of 68.6 m/s is a mere 1/200th of the kick for launch."

Yes, it may appear to be insignificant. There are a number of reasons why it is not insignificant and there is a number of ways to show why it is not insignificant. The simpliest way to look at it, is to examine the amount of fuel used by a rocket to get to a speed of 68.6 m/s.
With a large rocket this is quite a substantial amount rocket fuel (and overall rocket capability) to get to this speed. With a smaller rockets it is not as significant or impressive quantity. But counteracting this "dimishment of effect", a suborbital rocket is going for a much less total delta-v, therefore instead of "1/200th of 11.3km/sec" your needed delta-v is less than 1/2 of the 11.3 km/sec and could be closer to a 1/3 of this total, thereby increasing the 1/200th to 1/100th-1/60th.
But we are looking at this complex problem relatively simplistically. For instance, the escape velocity of 11.3km/sec, you cited is not the same as the delta-v needed by a rocket- it doesn't include gravity losses, and resistance from air friction. In other words a cannon or anything which quickly accelerates, would be closer to 11.3 km/sec than a rocket- which as a slower acceleration. These "losses" in a rocket add "about" 2 km/sec to the 11.3 km/sec number.
In rocket design one must balance the total mass of rocket and payload, against engine power, and efficency of the rocket fuel in providing thrust. So simply stated if your rocket engines provided a million lbs of thrust, you want the total mass of your rocket to be significantly less than 1 million lbs- if your rocket weighted 1/2 million lbs at lift-off, then you would have 1 gee acceleration (over the 1 gee of gravity). No large rocket as a 1 gee take-off acceleration, nor would any rocket have say a .1 gee takeoff speed (it would simply waste too much fuel going just above it's "hover" speed, plus it's dangerous because it needs to balance and any reduction in power would result in the rocket hitting the ground and blowing up. The total mass of any rocket going into orbit or escape will be mostly composed of rocket fuel- it's somewhere around 90% of the mass of the rocket (though with sub-orbital vehicles this mass fraction is much lower [and much more easily "allows for" reusable rocket designs]). With rockets that go into orbit, you typical take-off acceleration are generally around .6 gees. With sub-orbital rockets there "might" be a higher acceleration at take-off, though the Redstone sub-orbital rocket was actually around same acceleration as larger rockets: Liftoff Thrust: 37,470 kgf. Total Mass: 28,440 kg.
http://www.astronautix.com/lvs/redstone.htm
Now if you want a reusable sub-orbital space vehicle, generally this means you will have a less efficent rocket in terms of "delivering payload" than compare to an expendable rocket- a rocket "drops" stages in order to improve it's efficency.
Any rocket engineer that can get "any" improvement in a rockets efficency, generally consider this good. But safety is also important- rockets "blowing up" is far too common with rockets. A pipelauncher would have to be safe.

"If your method introduces more than 1/200th risk cf. a conventional launch, then it is not worth considering."

I think a pipelauncher *should* be able to actually lower launch risks as compared to a static pad. Though anything done for first time does have added risks.

"I suggest that you do more work on reliability, and think whether a static launch from Kilimanjaro or Mauna Kea will be better than a boosted launch at se level."

A pipelauncher would cost less to develop and less to operate than compared to launching from Kilimanjaro or Mauna Kea. Also a rocket could lift more payload if launched at sea level with say, 100 mph of added speed than compared these higher altitudes from static pads (if same distance from equator as launched from pipelauncher)

"Look up Lake Titicaca, when you have spare time... "

This lake might work, but probably most important aspect is the shipping cost to this lake. This can be simplified by one question, "What is the price of gasoline at Lake Titicaca?" Of course, you also need LOX, liquid air, kerosene (or other types of rocket fuel)- and of course far more importantly, permission to use the lake as a launch site.