A cool thing to add would be an auto progress button. Basically a button that brings you to the next area every time you complete the objective, until you are defeated.
Usually if the game won't save, the problem is your browser blocking third-party cookies. Are you using Safari or any privacy-related browser extensions? Make sure "www.swarmsim.com" has permission to set cookies (localstorage). I'll get you a similar save if you message me with what units you had, and your progress sounds realistic.
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Agreed and it is already in the game. It is available after reset and works exactly as you describe.