Egg bound or other? In need of advice!

Howdy. My Americauana (1 year old--has been laying consistently eggs for 7 months, every other day) has developed a "condition." Eggbound?Here's the history--3 weeks ago she laid 2 really large and weirdly shaped eggs. Then, she laid an egg without a shell (her eggs up until this point have always been hard, she gets plenty of oyster shell, and other calcium); then, she had yellow yolk coming out of her. After this, the next day or so, she started displaying all of the egg-bound symptoms--a bit listless, eating little, funny stance. I've tried a warm environment, palpated her abdomen, and felt inside of her vent (there didn't seem to be anything up there...?). After this, she appeared on the verge of dying, then within 24 hours fully recovered to her former spry self, minus laying any eggs. After a week and a half of "recovery" she just laid an egg (also really strangely shaped--long, thin), and now today is displaying the egg bound stance...trying to expel something. There is some liquid fluid (transparent and watery) coming out of her, as well as a long strand of slightly solid whitish-yellow membrane (I tried gently pulling on it, but it seems stuck, and I don't want her to prolapse). It also appears as if she laid a very small white membrane (but still has this other thing hanging). She seems uncomfortable. Any advice as to what's going on? How to remedy it? I assume if she recovers like last time that this might perhaps be a repeated problem. My other two chickens are fine and healthy (a Rhode Island Red and an Australorp).
I would greatly appreciate any advice.

Have you tried soaking her in a bath for short periods? Sounds like she may have the leftovers of an unlaid egg hanging in there.

I remember you having the problem before and you said she had a problem with her one leg.

How is she doing?

Her leg can be affected as this can cause pressing on the nerves that control the muscles to the legs.

You could also try putting her on a warm wet towel in a box or small cage with a heating pad or warm water bottle (the kind you use in the winter to warm your feet in bed). Temp needs to be between 85-90F and humidity 80%.

Give her some electrolytes and vitamins (no iron) or gatorade to increase her energy level.

You could also fill your bathroom with steam from the shower or bath and put her in the bathroom.

Fill a spray bottle with very warm water and cooking oil and spray that on her vent area.

Let us know how she is doing.

I found some more information for your on an older post, perhaps you could try this in addition to what I suggested.

"Give her a TUM (emergenciy substitute for calcium gluconate that vets give with eggbinding) ... also give her three drops of POLYVISOL (without iron) for a week then taper off as vit D3 is necessary for calcium absorption and is often assoc with soft shells."

This is information supplied by a bird breeder;

"In order to pass a developed egg, the mucus membranes around the vent must be soft and flexible. It is the fat based vitamins that are primarily responsible for this condition, most notably linoleic acid (Vitamin F) and Vitamin A. Without these essential nutrients, the oviduct becomes dry and hard. Most avian vitamins do not include the fat based vitamins, so it is important to supply a separate source for these vital nutrients. These essential fatty vitamins can be found in many of the oily seeds such as safflower seed, sunflower seed."