You're apparently unfamiliar with the current state and direction of spaceflight. Suborbital vehicles take off like airplanes on runways, or vertically from concrete pads--no "gantries" required. Mojave, for example is a spaceport, as is Burns Flat, Oklahoma. One is being built north of Las Cruces, New Mexico. Others are planned in Australia, Singapore, Dubai, etc. Their operating characteristics and costs are similar to those of aircraft, since they only go to Mach 3 or 4, and only to a hundred kilometers altitude (currently). They'd be ideally suited for this type of mission, which only needs to deliver raw materials to the stratosphere. With a sufficiently large fleet (a couple dozen vehicles per spaceport), the estimate of a hundred flights per day seems quite reasonable.
Such a project would never be done with conventional expendable rockets for exactly the reasons you state (though you also don't seem to be familiar with the fact that Titan is out of business, and that it would have much greater payload to suborbit than GEO).
You avoid doing the math, postulate concepts that come off as idiotic, half-baked, naive, incomprehensible, simplistic, and dangerously uninformed.
You propose a not-yet-built-still-on-the-drawing-board concept vehicle to do this.
"Couple of hundred flights a day" you say? Why not a thousand flights a day? Where did you get this figure? Out of thin air? How was your figure computed?
A less wacky concept would be to launch enormous Beach Umbrellas. - each a mile or two across - to shield us
You avoid all logic by reducing your postulate to an unsubstantiated and unprovable claim.
Show me your Math.
How many Sub-orbital vehicles are there in the world? What is the time lag between flights? How soon can the first Sub-orbital ship be ready? Where are the crews training?
Why not a Mag-Lev rail gun. There have been many studies and Computer simulations where the practicality of such a sub-orbital delivery system have proven moderately feasible