In other words, the larger the comet, the better.
You'd need a fairly obvious number of rockets to impart that sort of velocity change on a large one, right? And if you're doing it to a pebble, it doesn't matter too much?
I don’t think so? If you’re bringing in a big one you need more engines to push it into the right orbit to start with, so I think the risk is always things that scale up directly with the comet’s mass, e.g. “the engines are misaligned by $foo degrees”.
Also, a pebble in space terms is still a potential city-killer, and no nation in their right mind is going to want to let a private company — not one of their own, let alone a private company in another nation if they have even the slightest say in the matter — wield that kind of potential: https://en.wikipedia.org/wiki/Meteor_Crater
We watch asteroids zing by regularly. The ones we know about have their chances of hitting calculated years or decades out.
And the sort of rock that could shift 67P from a safe to a dangerous path (LEO to 45 degrees one year ahead) would be about 13 metres radius. The Wikipedia citation is 5 years old, so I don’t know what we know today, but in 2016 the estimate was we only knew somewhere around 1.3% of asteroids between 40m and 3.5m diameter (and 0.003% of smaller than that, because things get harder to spot as you get smaller).
Wiki: https://en.wikipedia.org/wiki/Near-Earth_object#Size_distrib...
ArXiv link because the citation in Wikipedia was giving me a server error: https://arxiv.org/pdf/1604.06328.pdf
If it was a naïve straight-line path with no funky orbital mechanics to make things even harder to get right, the difference between hitting the Earth at 90° and missing by the orbit of the moon is a sideways delta-v of 13 m/s one year in advance. The sideways Δv between a 45° impact and LEO, 7 days in advance, is 3.5 m/s.
I’m curious: Even ignoring engine errors, given near-Earth solar orbital velocities, what’s the mass of the smallest asteroid which, if it impacted that comet 7 days before the comet reached Earth, could cause it to hit Earth? For whatever orbit you want to put it in, and whatever mass of comet you want to suggest using.