I have a brown-headed parrot (cousin to the Senegal) and he weighs 135g. My vet says his weight is normal. He weighed around 125g when we adopted him from the rescue but he was sick at the time with pneumonia.
I know that your vet and local store say she's large overall (length and head size) but even with that in mind 198g is pretty extreme!
I understand that you want to address his weight but have you asked the vet about a formulated diet? There are specific diets formulated for overweight parrots but they are only available through a vet. I'm not pushing Roudybush here but just using it as an example: Roudybush has one called "Formula AR Reducing Care - Formulated to provide nutritional support during a weight reduction period. This is a healthy alternative to feed restriction. This diet is a low energy, low fat, high fiber formulation to safely decrease caloric consumption."
Beyond that I agree with what others here have said. His diet needs to be radically changed. He will probably be mad in the short-term that he's not getting as many "yum yums" (how adorable!) but in the long run he'll be far better off because an overweight parrot is prone to very serious health problems.
You are right to offer him a varied diet; it's not so much what you are feeding but the ratios.
For example, I feed my birds Harrison's pellets and Harrison's instructions are "supplementation should be limited to no more than 10% of the overall diet." If I had to estimate I'd say my birds' diets consist of 80% pellets and 20% supplementation. The 20% includes (from largest to smallest quantity) vegetables, grains, fruit, and nuts.
A bird is very much like a small child in that if you offer it a variety of things it will pick out what it wants (fatty and sweet foods) and not what it needs (pellets and vegetables).
If you or someone else is home enough to be able to restrict feeding times (as opposed to just leaving food in his cage all day) that would probably be best. If that is not possible the only thing that should be "free fed" is pellets (and even then you want to try to offer only what he needs). Anything else (grains, fruit, and especially the nuts) should not be readily available.
Don't rule out flight just yet. It may not be feasible now but some of the problems you described can potentially be addressed with clicker training.
For example, my GCC is a re-home. In his first home the husband hated him but would be left "in charge" of the bird while the wife was gone. She told me herself that her husband would leave the bird in his cage for three (or more) days at a time, and as a result he hated men and was very aggressive with my husband for about a year. We worked with him and 3 1/2 years later my husband is actually his favorite now. I mean he loves me, too, but if my husband walks into the room my GCC immediately ditches me in favor of him. Ha!
My brown-headed parrot doesn't like me very much (as I said, he was sick when we adopted him and he learned very quickly to hate women because all the vets and vet techs that handled him were women) so I am the one who works with him when we train. He still doesn't really like me very much but I've definitely seen a noticeable improvement in his demeanor toward me since I started clicker training him about two months ago (for example, he stopped lunging at my hands).
While you're cutting way back on the treats, you might also want to consider switching up who offers the treats.
If your husband is the only source of "yum yums" Bibi might start to re-think the relationship.
