Thank you! Very glad you enjoyed it. ◕ ◡ ◕ I wrote a reference to the birthday date with River but it got cut. It came in the montage sequence on the ice at the start of the episode when Bill is running around trying everything. She twigs that the Doctor has been to the frost fair before and he replies, “Oh yes. A few times.” A stunned Bill absorbs that and we cut to:
The scene might have actually been filmed (not sure) but I do understand why it was cut. You said it yourself – the important thing here is to focus on the present-day story. A mention of River doesn’t move the plot forward, or even advance Bill’s understanding of the Doctor to a significant degree, especially compared to the more solemn things she comes to understand about his past just minutes later.
There might even be another reason it was cut. Perhaps Steven decided Bill should learn about River in some other way further into the series. If not, then if you want to you can always extrapolate from the Doctor’s “Oh yes. A few times”, and assume that Twelve took the opportunity to tell Bill about his wife in between scenes.