Jeremy: I have a *general worldview that when choosing between foul up or conspiracy go for foul up. I suspect what happens is you were fortunate in your install in that the other people using it were not doing anything very taxing whn your students were accessing it. Then some other people sharing the host started doing some intensive tasks and the performance for your account went south.
It might well have been that a few minutes, hours or days later performance would have come back if that other user had stopped whatever it is they are doing.
I have had success with cheapie shared hosting with about 20 users, but it was with the knowledge that at any second the performance might go horrible because you never know what the other people are doing. For the benefit you get from a Moodle VLE $50 a month does not seem a huge expense in the overall cost of education.
Having said that the cost of any hosting I use tends to come from my post tax money earned as a part time teacher so it's shared hosting all the way for me and dammn the performance.
*(recent global/spy news events has started to rebalance my view on this)