Re: Pointing problem
"I can't see a reason for transport beams to be swept at all, unless it's hard to turn them off."
Yeah, along with the point made by Tom7, fast bursts of energy don't seem to make much sense as a solar-sail propulsion system at all.
The issue is that no material is perfectly reflective and this limits the amount of energy that can be beamed at the sail and its probe; beam too much energy at it and you'll simply vaporise it. At the same time though, a single burst of energy, at a level safe enough for the sail and probe, wouldn't be sufficient to effectively power it.
Another problem with the propulsion system idea is that if the source is a laser then you'd expect the bursts to have a very narrow bandwidth, which doesn't seem to be the case.
Although most of the FRBs recorded to date seem to be one-off events FRB121102 appears to have been the source of a total of 17 (non-periodic) FRBs since 2012 but even this source really doesn't seem like a plausible candidate for a propulsion system.