The simplest, least invasive way for them to fix it would probably be to just FAQ, "Does the space outside of the legal playing area constitute an obstruction? Yes. Yes, it does."

Can't boost or barrel roll into an obstruction, so problem solved.

This might be the simplest way to take care of the boost/barrel roll problem. Then when we go back to the OP's original situation (template off the edge but final base position OK) we find that the rules for obstacles would require that ship to a) skip the Perform Action step, and b) roll for obstacle damage. A fair trade to solve a sticky problem, I think.

I'm not a fan of adding extra punishment to situations that currently don't have one for being legal (OP's original question).

The simplest way, IMO, would be a simple FAQ answer:

Q: Can a ship perform a Barrel Roll or Boost action if its base would end partially or totally outside the play area?

No

That's all.

Since Boost and Barrel Roll actions set off Proximity Mines like maneuvers, it stands to reason (IMO) that ending up outside the play area using either would have the same result as if it happened from a maneuver.