I suspect that your hen is suffering from salpingitis, and the article you read is a good one. To me, that mass looks like lash material. The difficult thing is that it's not possible to see inside to see if it's just a small bit, or if it's attached to more that is farther inside. Sometimes that material can adhere to tissue and if you were to pull it, it could cause a prolapse, or worse. Some birds will pass small bits, some pass large pieces, some pass nothing. I've seen some where the material is a long piece that is formed to the shape of the oviduct, those generally cannot pass. If vet care is an option, that might be best, if she's not able to pass this. I would continue with the calcium to see if it helps. As long as she can poop, then it's not blocking that. If it becomes blocked it will be fatal rather quickly, just like egg binding. Whether to try antibiotics is up to you. For that, vet care is best as they can test to see what antibiotic might be most effective. If that is not possible, then most of the time Baytril (enrofloxacin) is recommended. https://jedds.com/products/enrofloxacin-10?_pos=1&_sid=5a0a72324&_ss=r
Salpingitis is very resistant to treatment, especially when it's more advanced, which I suspect this is based on how long you say she's been having issues. Sadly that is often the case, they are very, very good at hiding symptoms early on.
I have had birds live 18-24 months once it's known, I've also had many pass much quicker. It's hard to predict. None of them has ever laid again.
Salpingitis is very resistant to treatment, especially when it's more advanced, which I suspect this is based on how long you say she's been having issues. Sadly that is often the case, they are very, very good at hiding symptoms early on.
I have had birds live 18-24 months once it's known, I've also had many pass much quicker. It's hard to predict. None of them has ever laid again.