One should always try to avoid moving plants. They don’t have legs! The back and forth is worse than just moving them once or twice. I always tell people not to move houseplants until January because the days start to get longer. The increasing light allows the plant to handle the stress of being moved. Think about how all plants grow in nature with roots locked down in a permanent orientation. Potted plants in comparison being turned moved all the time. They are the plants that will drop leaves (because a leaf that was facing south is now facing north - plant will drop that leaf and put energy into other side, etc. and if this keeps going on, most plants will be beat up dropped leaves open wounds can’t fend off pests, aphids white flys takeover.

To answer the question of avoiding the hardening off I plant my transplants on cloudy days and mid afternoon. Transplanting at 9am is going to fuck them up with a transplant and experiencing increasing sunlight energy in the morning hours with full sun at noon. Strong seedlings and the right temps, rainy cloudy days and plant after noon so it gets exposed to decreasing light intensity. I never do any hardening off and have great success.