Railgun
Jowan knows Fireball XL5, and that's got the railgun.
It has a loading bay rail system on which factory units are built. The loading bay can merge streams of completed factory units onto a launch rail. The launch rail has many acceleration points which kick each passing unit faster. The departure velocity is sufficient to put each unit into Mercury orbit. The orbit needn't be high, there's no atmospheric drag to consider, just don't graze mountains.
Each kicker is powered by one or more railgun power storage units and direct Surface power collector connections which can be wired rather than broadcast. The power storage augments and smooths the kick. The initial idea is a bank of super-capacitors.
A factory unit of 20 tonnes leaves an 84km rail at 4.1km/s with an acceleration of 100m/s2 after 41 seconds. There is no atmosphere to plane on. The kicker could lift the unit from the rail as well as kick
Moving the decimal points, an 8.4km track at 1km/s2 after 4.1 seconds sounds extreme but it's the same sum. It's all dependent on the power input.
So, how many units per second must one railgun handle?
Specify a quarry 100km wide, with rails every 1.56m apart merging 1m wide (4m long) units onto the railhead at the sharp end. The quarrying front gets further from the railhead at a rate dependent on how long it takes to build a factory unit. There are 64,000 tracks and a depth of 16 points merging onto the railhead.
If the minibots on a single track can build one factory unit from start to finish in one day, like Liberty ships, that's 64,000 launches a day at 0.75s separation. A railhead 8.4km long will be accelerating 6 units at any moment. If unit production takes longer, then the railgun has fewer units at a time. The advantage of the higher of the two nominal accelerations is that the final section of single track only has to handle of the order of 6 units at any given moment instead of 60, and everything is lighter.
Either way we may end up having to use cold night-only launches to get rid of the heat and maybe use superconductivity. This would stack production on the ground or halve productivity.
Each railgun, after 10 years, is 100km wide and 15km long if it goes back 4m per day. 1% of the planet surface can host 500 railguns. That's a limit of 1E11 mirrors, which is 2000 times fewer than a 1% target. That feels about right, given we've only skimmed perhaps 100m off the surface of 1% of the planet and the initial requirement is more like 200km.
This would be quite an engineering shortfall, I'm not sure where there are orders-of-magnitude slack to take up. On the positive side it yields 3E20W compared with current consumption worldwide of under 2E13 (20TW). The reduced swarm output of 500 railheads is 15 million times higher than that.
We might be getting closer to a viable scheme with this. Even one prototype railgun quarry would do it. I think one prototype railgun and a reduced swarm is an ideal 2040 target to be honest. That's a 100m deep quarry, 100km by 25km, we've specified the rail links and the rate of delivery, we're a step forward. We might be closer to preserving the essential vacuum too. A ten-year run of a single railhead at full output still offers a swarm capturing 30,000 times more power than the world currently consumes.