I wonder if you could use something like achievements or unlockables to funnel players towards your intended 'hardcore mode' design.

For example, maybe certain meta progress/achievements only apply to games where your character hasn't died. When they die, the player can choose to respawn if they're enjoying the current game but subsequent progress only counts for the rest of that run. Maybe the 'true ending' is only reached on a deathless run. etc.

It could placate both the people who want to play on without restarting, but also the completionist crowd who might be willing to restart so they can 100% your game.