Oh! My vet calls it Deslorelin, so I didn't recognize the product! I looked it up and it is the same thing.

I've had two birds in the past on that medication before. These reproductive issues are just crazy.
My duck is Thimbleberry, also a pekin. Thimbleberry's vets advised us to follow 4 environmental changes.
1) Dietary - Thimble eats mostly scratch and some Mazuri waterfowl maintenance. When she was younger and having reproductive issues she had strictly only scratch. Now that she is older (6.5) they think she needs the extra nutrition. She also forages a little. The theory is that if there is a food shortage it is not a good time to have babies.
2) Lighting - Thimble has a very strict 10 hour daylight schedule. Every single day. We have a timer on the light in their barn room. We NEVER put them to bed late. We put tar paper over every single tiny crack between the boards that lets light in. The theory is that if it is days are short and it is winter it is not a good time to have babies.
Thimbleberry has two "sisters" and I put them to bed with her. I figured they can take one for team Thimble and go to bed early so that Thimble isn't stressed out and by herself. They are used to it and I don't think they mind.
3) Hurricane protocol - Daily we destroy all nests built and get rid of eggs (from the other ducks). We allow no dark cozy cubby places for building nests. Frequently, at least once a week, we move all their stuff around. We put their food bowls in entirely different places - like the complete opposite side of the aviary. We put their food storage bins in completely different places. The theory is that if a hurricane just came through it is not a good time to have babies. Yes, the vet told me to do this!
4) Petting - Don't stroke her down her neck, back or tickle her under her tail. That can stimulate egg production. I do touch her feet, bill, and stroke her chest.
It isn't easy, but we have been doing this for a year and Thimbleberry has never felt better in her entire life. Her vets recommend doing this for her indefinitely as Thimble has had ongoing various reproductive issues for at least 5 years now.
Last summer she was storing dozens of egg follicles in her abdomen in different stages of development, from very small to quite large - but she wasn't actually laying any of them. In addition to that she was very tired. When we went for a walk she could only forage for a couple minutes before taking a nap. After implementing the environmental changes I could see her becoming more alert and having more energy within a week!! There was a remarkable difference in 2 weeks. In 4 weeks at her check up the doctor could see significantly fewer follicles when they performed an ultrasound. In the following months I saw continued improvements in her energy levels. Despite the fact that she is now 6.5 years old I have never seen her so energetic!
We did this a couple years ago as well, but then only for about 5 months. It seemed to just turn her reproductive system right off. She was laying then, but the eggs were getting stuck in her and she was having funky prolapse issues with weird masses, too. She had to have surgery to save her life - they sent us home from the hospital with instructions to start environmental changes and we had no more reproductive issues, until the next spring when the environment was back to normal.
I definitely recommend discussing this with your veterinarian before starting these changes. But it has worked so well for me and Thimbleberry. We really thought she was going to die. The vets told me that it doesn't always work, but that sometimes it does. That if it didn't work we would try hormone injections and implants, and if that didn't work we would try to spay her. But... of course spaying doesn't always work and has complications.
I'm not sure if any of these recommendations can help you. Thimble was already thin, and they wanted me to restrict her food even more. I did because she was going to die anyway if I didn't. Thimble doesn't mind going to bed early because she has her sisters. If she was quacking in distress for hours I'm sure the stress would pose a real threat to her health and not be worth it. At that point you've got only the hurricane protocol and not petting her down her back. My feeling is that those are the less influential of the 4 recommendations.
But Thimble has had no reproductive issues for a year now. I'm taking her for a check up in 3 weeks. I feel that she has lost more weight and am going to ask if they want me to continue restricting her food. She clearly feels great, she even flies a little to greet me. She used to be so tired she could barely walk. I'm concerned that she is too thin, but I don't want to let her eat more and have her die from reproductive problems.
Its so frustrating and overwhelming. Sorry I wrote you a book.