Let's talk about this...
This is a Frame Challenge.
Are you trying to force a policy, or are you balancing technology and economics with policy?
When humans ignore economics and technology to implement policy they get... well... weird, bad, not-very-useful results. I remember back in 2003 my brother calling me and asking if it was possible to take advantage of a U.S. government grant program that sought to put retail-grade and retail-cost solar power onto (I kid you not) Walmart's shelves. The program was literally asking for what at the time was magic: a low-cost solar solution that could be bolted onto your roof with no more skill than is required by a hammer to solve your power needs and thereby get rid of all the evil coal, natural gas, and nuclear power facilities.
When I stopped laughing, I explained all that to my brother.
That grant program was an example of ignoring economics (the cost of manufacturing solar arrays) and technology (the ability to build self-contained and sufficiently efficient solar arrays small enough to solve individual household needs) to implement a policy (everything would be green today if we just convince people it's true!).
In reality (and that's a statement that starts bar fights over here in the States), policy, economics, and technology must work together to provide a solution that works today with an eye toward a better solution tomorrow.
Your question kinda feels like you're trying to ignore economics and technology to implement a policy.
A price must be paid
Simplifying things a bit, it takes 3.29x107 joules of energy to lift just one kilogram into orbit. The Space Shuttle on the pad weighs 2,041,166 kg. So we need 6.7x1013 joules to push it into orbit.
You can't argue with that. That's physics. That's the price. What's left is to decide the economic, technological, and political balance that pays that price. If you graph the value of those three variables needed to pay the price, you'll end up with a bumpy surface that trends toward infinity1 as any of the three variables trend toward zero (even for policy... think of it as, "despite what the government wants..."). Rationally, the goal is to find the lowest point on the graph and use that combination of economics, technology, and policy to launch your craft.
Since when are humans rational?
Which brings us to your question. I upvoted @ths' answer because his is the fundamentally correct answer. But I'd like to express it with my favorite worldbuilding.SE quote:
"Can you launch an ICBM horizontally?"
"Sure, why would you want to?" (The Hunt for Red October)
Could you push a ship fast enough with air breathing engines to shoot it into space? Sure! At a price. And it's a pretty high price. Your biggest problem is that air thins with altitude, which means you need to create sufficient momentum lower to the ground, which means you're fighting air resistance longer than you have to... you get the picture.
Science is a... um... somewhat crotchety lady
Let's look at this in a cold-hearted way: you haven't created a fuelless solution. Not for any aspect of what you're doing. Fuel is being burned, you're just not who or what is burning it. In this regard your solutions are like solar power. The sun is burning the fuel, you're just taking advantage of it. And you want a solution like that, right?
Air-breathing engines ain't it. They'll require fuel. A LOT of fuel.
A better solution for you would be to create a space elevator powered with solar power. No fuel in ways similar to what you've already presented. Just attach the ship to the 37,000 km long winch and haul it up to orbit.
1 In other words, if you want those joules for free (no economic payment) you need either infinitely capable technology or infinitely flexible policy or both. Do you want it with little or no tech? Infinite cash (so you can build that tower!) and/or infinitely flexible policy (so you can rob your neighbors for the cash to build that tower!). Do you want it despite what the government says? Yup, infinite tech (so you can build it w/o government assistance) and/or infinite cash (to bribe the government!). This all makes sense when you think about it.