+1 for BA001. Worth checking availability in general though before getting excited as we know that this hasn't been great so your options may be limited.

Would (if you can) chose a day that is less busy (I am flying on Monday and 001 is almost full) so maybe a Tuesday, Wednesday or Thursday outbound - I have been on it once with 7 pax which was great especially with 3 crew. if the load is particulary light, you might have a row or two at the back to yourself to do it.

Good luck with the planning - sounds like a great trip (and hopefully she'll say yes )