“Well then, shall we act like other men? Shall there be no distinction between ourselves and the world?”
Yes, a very great one; let men find that we are unlike the common herd, if they look closely. If they visit us at home, they should admire us, rather than our household appointments. He is a great man who uses earthenware dishes as if they were silver; but he is equally great who uses silver as if it were earthenware. It is the sign of an unstable mind not to be able to endure riches.
Seneca,
It seems fortuitous at the end of the first week of our correspondence we being with an exhortation to continued study, and congratulations of such. Fate is a funny critter, at times.
However, you promptly moved on to my chief concern with your interpretation of our school. I agree that a great man uses earthenware as if it silver, and the reverse also. Yet, your final sentence in the passage I’ve quoted smacks as a justification of, if you’ll pardon my frankness, the clear opulence in which you live.
Shall we line up, Musonius, Epictetus, and even Marcus to see if they live in a way such as you’ve posited? I think you’ll find your position wanting. Epictetus extolled Diogenes of Sinope, the Cynic, as a philosopher par excellence and the very model of the Sage!
Stoic askesis requires that we actually practice being self-controlled to inculcate that virtue, that we be just, courageous, and wise. It is not, as Socrates posited, merely enough to know about virtue; to know it and have it we must act. We must train.
The opportunity for self-delusional indulgence is simply to high to skimp on the training for the average prokopton. Indulgence trains our moral will.
It’s possible, sir, that you are a unique specimen of philosophy, and I do not levy that you might not be. That is not for me to say. But as for me, and for the multitudes of philosophers who aspire to our mutual School: we must train.
Epictetus does not say to us to examine our books, our writings, or our words. It is not how well we handle the syllogism, or grok the readings of Chryssipus.
He says rather something else:
“Watch your own conduct thus and you will discover to what school you belong. You will find that most of you are Epicureans and some few Peripatetics, but with all the fibre gone from you. Where have you shown that you really hold virtue to be equal to all else, or even superior?
Show me a Stoic if you can! Where or how is he to be found? You can show me men who use the fine phrases of the Stoics, in any number, for the same men who do this can recite Epicurean phrases just as well and can repeat those of the Peripatetics just as perfectly; is it not so?
Who then is a Stoic?
Show me a man moulded to the pattern of the judgements that he utters, in the same way as we call a statue Phidian that is moulded according to the art of Phidias. Show me one who is sick and yet happy, in peril and yet happy, dying and yet happy, in exile and happy, in disgrace and happy. Show him me. By the gods I would fain see a Stoic. Nay you cannot show me a finished Stoic; then show me one in the moulding, one who has set his feet on the path. Do me this kindness, do not grudge an old man like me a sight I never saw till now.”
— Epictetus, Discourses II.19
“Show me a man moulded to the pattern of the judgements that he utters.”
While we are warned not to pretend to “the philosopher’s mien” too quickly (pun intended), a beard and tribon do not a Stoic make: our judgments clearly should shape our lives, and the indifferents with which we surround ourselves as well.
It is with thoughts of the pious, ascetic, virtuous Sage in mind, that I bid you a very fond farewell.
Mountain Stoic 
I agree with you about the necessity of training but I think Seneca’s point is that if you are adversely affected by external riches then you are still being adversely affected by an external and letting your happiness depend on an external rather than virtue. Although Seneca’s elegant language is very different from the terse statements of Epictetus, they are very close in meaning.
This is actually one of my favorite ideas expressed by Seneca, and for the exact reason that John mentioned. We should be indifferent to all externals–including wealth. To be concerned with whether one has too much or too little wealth demonstrates that a person is not actually indifferent to those things at all.