I just threw in the God Mode cheat and breezed through the level to get back to where I was. In the developer console (~), input e_cheats true and god 1 whilst in-game. You'll lose access to the achievement, but you'll at least have beat the game.

Also, I discovered that if you find you're about to run out of time, you can quit out and reload your save file, and you'll be back at the last phase of the boss battle (where it last autosaved), allowing you to give it another go. It doesn't actually autosave until you hit the "Restart" button, so when you reload your last save, it'll be after you beat the two mechas. This also works to bypass the gameover system (by allowing you to reload your last save as opposed to starting the entire level over), throughout the rest of the game, too. Just too bad I didn't find this out until I made it to the final level.