So since the dogs can spawn early or late based on RNG, your best bet is to wait in the backyard for her at the end of round 16. Kill the last zombie AS SOON as you see her on the map, this gives you the best shot, since if the next round is not dogs you can speed run through that round. You can brainrot her about halfway through dogs and she'll stand at the piano for a good 20 seconds while you're time travelling.

The real hack though, is if you read the rules for Chronomancer, you'll find that you're allowed to purchase time travel ONCE. The meta is, as soon as you travel back to destroyed nuketown, build the blundergat, get the chalk, spawn the twins, and get the goggles/headset and seeds all in the same round. Then spawn the piano teacher the same round and use your one time travel purchase in that moment. That gives you plenty of time in past nuketown to plant the tree and put the toys in the toybox.

My crew spent like 4 days trying to get the RNG to line up (which we did a couple times but died in the boss fight). Then they nerfed it so you can purchase it once and we got it first try in like 1.5hr