what about reapers.
One like Sovereign who was patrolling the galaxy between cycles could easily become a carrier for eggs. Not even counting the purges.
If we go back a million years, threshers likely live anywhere from 1,000 - 10,000 years based on Kalros, and would need such time to evolve.
One reaper randomly passes through a spore, which is likely evolved as a way to spread younglings to the far side of the planet so as not to compete with their parents. This is a known method that some plants use to a lesser extreme on earth, so on the Krogan home world where there is already too much competition this would be an ideal strategy for such a massive creature.
Lets say it picks up 1000 eggs,
Reapers move fast, and far. So the reaper could easily sow 6 plants over the course of a cycle, and as these are most likely developed and habitable planets you now have 7 places with reaper activity and thresher maws.
Lets say that is it for that cycle. Next cycle they come back, and 2 reapers picks up spores spreading to 12 additional places.
The rate of spread would be
5*3^c
in 1,000,000 years, once every 50,000 years, that is 20 cycles, and at that rate of spread you are now dealing with up to 17 billion plants full of maws from the reapers alone, let alone all the various species in between spreading intentionally or not.
Even if the rate is much slower, it would still be amazingly fast to spread due to exponential rates of spread, as more planets to spread maws from means more potential to spread to new plants, which in turn increases the rate of spread.
It could easily happen even faster, if a small fleet passed through the system and a dozen ships picked up enough spores to spread to a planet or two each you could easily have a huge spread in a very short time. Imagine the huge Asari, Salarian, and Turian fleet that fought during the final battles of the Krogan rebellions, hundreds, if not thousands of ships stirring up the outer atmosphere, and traveling to dozens of ports afterwards, each and every one of them potentiating hosting the potential to spread thresher maws to any planet they passed, or to other ships in port that later carried them further, all thresher maws could have easily been spread by these unaware fleets in a few short years.