That's a great set up! I do my hardening off by putting the plants in an old cracked wheelbarrow (so the sides provide some protection from the wind), and then roll it into the greenhouse at night. Depending on temps and forecast I do it for 1-3 weeks and then plant.Hardening off can be a very important part of the seed starting process. I figure at least a week to do it.
Hardening off is another use for my XL dog crate. I put the crate out in the middle of the garden, put the pots in it, and drape a white sheet over the crate. Attached with clothes pins so it won't blow away.
The sheet breaks the wind and softens the direct sunlight on the plants. After a couple days, I take the sheet off for a couple hours. An overcast day is the best for their first foray into real sunlight. Each day, I leave the sheet off for a couple more hours. By the end of the week to ten days, They've been in direct sunlight all day, with the breeze.