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I did several things to get my goto working at decent speed:

1. Cache the danger value at each point on the second wave. That way, if you are able to reach the exact point before the wave hits, you don't need to look up the danger again.
2. Before calculating your second wave dangers, get all your first wave dangers. Sort each of these by danger, lowest to highest. That way, you can immediately break the moment your first wave danger exceeds your minimum first+second wave danger, because from then on it is impossible to get less than that.
3. Optimize your precise prediction as much as you can, then optimize it some more. Use FastTrig. Avoid divides. Cache values for cos/sin if your heading won't be changing any more. Compare squared distances instead of computing square roots.
4. Try to make your danger calculation as fast as possible. It gets called a LOT. If possible, stick everything in a 1D array so you just check the danger at that GF (or across a range) as you need it.

There's probably more, but I think these were the big ones.

1 and 2 looks a lot like transposition tables and pruning techniques used with success in chess engines. I was trying to find something similar in robocode for months, but failed.

You can cache square roots in 3 and only need to recalculate them when wave log is updated.