First of all, I make a living as an artist... but I am far from it. What you guys can do with paints and pencils I can only dream of. But, I stay busy while other artists go hungry. I even did a mural for an art teacher who was blown away that I was making a living at art while his students couldn't seem to do anything with it.
Now, I mention all of that to set the stage for my comment on your question. Marketing is huge in art and setting the right price is part of the marketing mix. I met with an Interior Decorator (way back in the day), showed her my work and then told her my prices. She told me that her clients wouldn't even consider having something done in their homes that was that INEXPENSIVE. They want things are quality and expensive. That is when I decided to become the best at what I do (I wanted to justify a price increase, not just raise my prices) and then charge for it.
After perfecting my murals... I quadrupled my prices and I have been busy ever since. I fly around the country painting (I paint the night sky with glow paints) my murals and people always pay me with a smile on their faces.
So, you mentioned asking $300-$350 for the painting... and if she didn't like that price, then you would offer her a print for less. That is the way I would approach it. That is basically a "take-away" sale and I'll bet you that your customer will go for the original painting, even if she flinches at first. The flinch is just a way to get you to drop the price. And, once she does the flinch... just offer her the print of the painting. So, you've countered her flinch with another option... but she wants the original and will want to get that from you.
There are people painting similar murals to what I paint (I say "similar" because they are just that... similar. They use glow paint and they paint little dots. That's as far as the similarity goes though :-)
) and they will charge $200 for what I get $800 - $1000 for.
If you drop your price to $150, then that is what you are telling the lady it is worth. If you do nice work... then price it accordingly. There is something called the "Snob Effect" and it is what that Interior Decorator was referring to. And, you mentioned that you know that this customer already likes expensive things. And, if that is the case and she likes your painting... then she will go for the original painting versus the print of it... because it has snob value.
I even had a customer tell me that she went with me because of that. She also saw that I had been featured on HGTV and the Fine Living network, as well as some magazines, which only enhanced the "snob value", but she also liked the fact that she was paying more than what most of her friends couldn't afford. And, she had me back out to paint a second mural for her.
So, to make a long post even longer... don't sell yourself short. Don't listen to people who tell you to price something because that's what they would pay. You set the price and be unique in what you do.