I just replied to what you have given as background information. Since you mentioned about a theological divide, I asked why, because to my knowledge all leaders are in alignment in this regard.
Br Up 3.5.1 and 4.4.22 explains Sannyasa as a voluntary giving up, not a forced one, not something one does on old age, due to a lack of energy. There is no reference to asrama dharma in the passage. Nor to old age. A person lacking energy due to old age, might still entertain eshanas/desires. As long as life lasts, he will find the means to satisfy the desires and will not simply abandon the sources of these desires. An ordinary old person might be devoid of knowledge of Atman. That is why the passage explicitly says of Sannyasam 'tam atmanam viditva' - (knowing that Atman).
If the rule was that Sannyasa must be taken only at the end of Asramas, Brih Up which repeatedly deals with Sannyasa, would have mentioned it somewhere. Whereas the whole treatment of Brih Up is to slowly explain that all worldly karma lead one to transient results of the 3 eshanas kind and only eshana tyagam will lead to Atmajnanam.
Moreover, in Jabala upanishad, if the concluding part is an exception, then that would have been mentioned explicitly.
You have said that Sannyasa is adopted when "brain faculties start giving up", when the body and mind will abandon. If that is the case, where is the logic in such an old person giving up his home and adopt bhikshacharyam?
Passion is diversion of excess energy into channels like kama, krodha etc. Then how can lack of passion be lack of all energy? That is faulty logic. Virajas is a state of equilibrium where a person diverts his energy away from all external desires, and turns it inward, to perceive the Atman as per the Katha Up sloka 2.1.1-4.
You are side stepping the issue. I never said you should connect vi-raja with Vairagyam. I said they are not dissimilar words. In all my earlier messages I connected vi-raja with eshana-tyagam which indicates detachment. If you don't want to connect vi-raja with Vairagyam, then don't. The issue here is with your translation of vi-rajas as 'lack of energy' which is a wholly different and incorrect meaning altogether.
You have translated eshana-vyuththanam above as 'abandoning the desire for children, wealth, world'
Do you see a problem in connecting the word Vi-raja with the eshana-vyuththanam above?
And the word Vairagyam, as you have translated above means, among other things, freedom, indifference to worldly desires. There is no mention in your translation, anywhere that Vairagyam must a characteristic of old age or an otherwise lack of energy. Indifference to something can be due to many reasons.
The expectation with marriage is, he should be capable of giving birth to children. Unless he is a Rishi like Veda Vyasa, a certain amount of passion is required in marriage. So if he goes on kasi yatra, he can be considered as expressing his aversion for the marital state, along with it's additional matters like passion for having children and relationships. This is in good sync with Brih Up 3.5.1 and 4.4.22 which expresses a parivrajaka as having aversion to children and other worldly pleasures.
I have answered reg Brih Up.
There are many other places in scriptures where Sannyasa is defined. Krishna defines Sannyasa in Gita 5.3. How do you align that definition with your concept of Sannyasi as an old person with fading faculties, lacking all energy?