This is, by far, one of the most miserable things to experience in a video game: being punished for failure. Failure is its own punishment, in the form of time lost since the last checkpoint and knowing that you failed.
Remove the reduced rewards if the player needs to use a continue! Even if they win after continuing, this is only punishing their failure with an increased chance of failure (which will be further punished) in the future vis-a-vis having fewer resources to spend on upgrades!
I actually think the game is overall much more forgiving than others. The whole multiple continues thing is already leagues more forgiving than, say, an Armored Core game which will make you start from the beginning if you die once. I get angry when I’m defeated but I usually just take notes and move on, maybe replay on a lower difficulty if I feel it was especially unfair.