At this point, you don't need to take your budgie to an unfamiliar room, that would likely add some stress on him, since he doesn't know the room and he can fly in a panic and crash land in the process.
You can close the door to his cage and place the play area right next to the cage or on top to the cage, if possible. This will give your budgie a sense of security while he gets more used to having out of cage time.
As he becomes more confident of his surroundings, he will start to explore the room and will gain appreciation for the time he has out of the cage.
Personally, I don't use food to train my pet birds, I mainly use my voice to connect and bond with them. Then again, I have been doing this for most of my life and it comes as second nature to me.
You can slowly wean your budgie off the millet during a training session and you can use more of your voice in a calm, positive, encouraging and reassuring way.
Using praise words in the right tone as a reward works like a charm and for your case, you can use a favourite toy as a reward to substitute for the millet.
From your description of how you got the budgie and the fact that he has learned words, it's clear that he was a very cherished pet and he most likely was closely bonded to the previous owner(s).
By continuing to interact with your budgie on a daily basis, you will eventually earn his trust and chances are high you will be good friends.
All things considered, one month is not that long and this budgie has already been through a lot, being lost and rescued by you, having a different family all this should be taken into account.
With patience and love and by taking your budgie's cues, you will know how to proceed with training. Getting frustrated and being negative will only hamper the bonding process and it's extremely important to provide a welcoming and positive atmosphere during the training sessions and every time you interact with your budgie.