This game is for stats nerds isn't it :P I'll echo what the other commenter said about the feel, layout, and art though, very nice.
For fun I calculated the odds of successfully pushing in all states where pushing is even possible. There are hundreds of permutations of those states, but only 16 actual states where pushing would be eligible. Lock the Fourth has the most possible rolling states depending on what the current sum is and what the highest die is at 12 possible states.
Much harder to calculate out the odds of a success for any given lock but at least the pushing was somewhat easy to puzzle out.
Fun fact, there is only one state in the game that has at best a 5/6 chance of a successful push. Three states that have a 4/6 of a successful push, five that have a 3/6 chance, four that have a 2/6 chance, and two that have only a 1/6 chance.
The odds of successfully pushing are better at the earlier locks, but then again there's way more runway ahead of you that could go worse and worse, so do you risk doubling right at the start??? And paradoxically, pushing at lock 1 can only save or cost you 1 memory, so it's not that impactful even though it might be one of the better odds... I like the decision points throughout :)
If you're considering alternate stretch goals too, it'd be neat to see a print-friendly version for download as well.
<3 keep up the good work, I'm going to tinker with a minor artifact subsystem I'll let you know if it's any good ;)