I'm sorry to hear you are so distressed with the situation with your conures. I think you have it figured out already you either want to re-home them or you want to change your life around and give them the time and love they need to be happier healthier birds who are less noisy.
Don't beat yourself up for the way things are going. You realize there needs to be a change for the birds so write down all the reasons you think you are not spending time with them. Pro's and Con's.
You just have to take a deep honest look at what you feel is your future situation and what's going to be happening in your life in the days months and years to come.
You mention you are now sharing a home with your partner does this change in your lifestyle seem to be affecting the way you deal with your birds? Your partner isn't really interested in them so it puts a stress on you if you see he covers the cage so you can have quiet time. It seems that time with your partner is more important than spending time with the birds you have had for a while now, this is normal and unavoidable.
You are working and traveling farther now and that means less time for the birds when you get home and want to unwind. Life is busy, you need to grocery shop and clean your home do laundry and work and maintain some time for yourself.
If the birds don't fit into that busy schedule easily anymore and you feel you can't give them what is most important then let them go back to the people who know them and will give them what they need. You can always call or email them and get updates and see how the birds are doing.
Life changes for people all the time and with those changes you need to be honest with yourself, do you really think you can make the time to give the birds the daily hands on they need or do you feel you can let them go.
I know it will hurt giving them up but personally I have a lot of respect for you if you make the decision to let them be re- homed. You are doing it for the well being of these birds, this is the best love you can give them.
Good luck with your decision.