You avoided the elephant in the room - the "she's not worth $400" issue - and successfully made the issue about YOUR budget without making her feel like she's over-valued her value.
I can only guess, but I suspect her thought process went something like this:
1. I need more cash
2. I do like him enough to have sex for cash
3. He's definitely better than far too many of the asshats I have been meeting
4. Better to keep getting less cash each meet, adding up to more cash over the long run, plus nice dates with dinner, travel, and other perks, then spend several weeks getting nothing while looking for a guy with a bigger wallet.
Now, given that she's not good with finances, planning, or achieving strategic goals (in other words, an SB), I doubt HER thought process followed the specific sequence above... but she got there nonetheless.
If you had taken the direct path by just saying "$400 is too high, I will only pay $250." She probably would have felt insulted and would insta-bail on you, calling you a cheap jerk.
Life is good
The Cat