Rather, I'm fairly certain that JA means the "Excepting one short period of her life" to refer to the "short period of exquisite felicity followed, and but a short one;" i.e., that time in which she was being courted by Wentworth. Surely in this period, with Wentworth by her side, she would have had the "happiness of being listened to, or encouraged by any just appreciation or real taste."

I think Lady Russell was pretty far from JA's mind in writing this sentence. Lady Russell probably would have loved to listen to Anne, and give her the attention and audience she deserves, but what encouragement would Anne have in that household to play for the amusement of the company? No, it seems much more likely to me to be a reference to Wentworth.