People tend to forget that the real complexity in orbital dynamics is in minimizing travel time, not in arriving to a particular orbital location. We try and find optimal launch windows for missions for two reasons; because there are people involved and we want them at risk for as little time as possible and using as few resources as possible (mostly relevant to the Moon missions so far), or simply to minimize the delay between launch and the need to manage on-site operations, like with Mars landers. We CAN pick and choose those launch windows, and our targets are relatively close, and we have a set boost vector we can use, and we minimize the amount of weight being used in all cases to maximize the effectiveness of those rockets, because the longer a delay, the more chance of something going wrong, and with these operations, that's usually a failure at the further points in the operation, meaning rescue efforts are highly problematic.
With an orbital mining relocation, the start point of the operation is still going to occur at a critical window, but the complex operations occur largely after we get boosters attached to the rock. And there's less of a time crunch; if a longer path is safer or more fuel-conservative, but takes years longer, that's an acceptable compromise. The other factor to consider is that while we've used orbital acceleration with our various long-range probes like Voyager and such, the converse, orbital deceleration, is also a thing. And conveniently, if we're talking about ending up in a Lagrange point, there's a convenient gravity mass nearby to use for repeated orbital braking maneuvers. You'd need boosters mostly for adjusting the trajectory for each pass, rather than trying to push the rock like a launch vehicle. It already has plenty of delta-V; the boosters are for trajectory adjustment and braking.
And while we might need a bunch more in the final approach, this is very much a case where we can send up additional boosters as the mission goes on; unlike most other missions, this thing would be getting closer to Earth for longer periods over time. If we're using multiple cycles of orbital deceleration to bleed off delta-V, each pass is another opportunity to load up more boosters (and I'm presuming we're designing them to not be retrievable).
Would that many boosters cost a lot? Sure. Trillions, though? The entire Space Shuttle program over 30 years cost $192 billion, and that was 131 missions total. And there's a lot that went into the Shuttle program that wouldn't be needed for launching unmanned missions like these. Once you factor in refining and setting up shop and everything, I'm sure the cost would be in the hundreds of billions, particularly as there's inflation to consider, but that doesn't seem unfeasible, particularly spread out over years.
The USA spends three-quarters-of-a-trillion-a-year on military bullshit. That price tag would easily cover this, in spades. So don't tell me the money doesn't exist. It's just that the USA prioritizes blowing up other human beings over space innovation.