[relaunched]

The earlier the investor, the more risk they took on. The same terms, if material progress has been made, doesn't seem like the same risk for the same reward.

What is right, and what you can get away with, aren't the same thing. You need more money, a first option to the original investors makes sense, unless the new investors are strategic. In that case, the current investors should understand that value and you can use that to justify the same terms (lower discount for the money, but additional discount for the strategic value).

Any restructuring should be as transparent as possible and you should spend as much time as necessary explaining your rationale to the parties involved. They don't have to like it, but they deserve to know what's going on.