I found that I didn't really feel very much pressure to move my base quickly. It felt more like the next task on the list rather than like the threat it was portrayed as. It was anti-climatic.
What I think would work better separate the player and biters with some kind of destructible, (such as a wreckage part), as a barrier that prevents the biters from pathing to the player. When the time comes to move the base, have the biters to start attacking the barrier. However, to give the player enough time to move, I would give the barrier a ridiculous amount of HP so they aren't immediately overwhelmed (for 3 minutes against 30 biters would be ~22,000 HP if I did the math correctly
).This would give the player a feeling of urgency and make it a more memorable moment, while still making it a relatively safe moment for the player.
