Rose has written elsewhere that her recipes don’t work well in pans higher than 2”. Since your pan is only half an inch taller, it might work if everything else was in order. If you’d like to try again, these are the adjustments I would make. First, I’ll confirm that we’re talking about the White Velvet Butter Cake, pp 46-7 in The Cake Bible?
1) Divide the ingredients in half since you’re making a single pan rather than two.
2) Make no other adjustment for going to your 7” x 2.5” pan from a 9” x 1.5”. The volume of the two pans is virtually identical.
3) You will, however, need to increase the baking powder by a small amount. The single 9x1.5” pan would use 2 tsp. Use 2 1/4 tsp instead.
4) Baking time is about the same, but probably at the lower end of the range (25 -35 minutes).
Good luck! Let us know how it goes.
p.s. added by edit
Just re-read your post and see that you were using the base recipe at the back of the book. Easier to make the adjustments in your case, if you use the recipe pp 46-7. But for future reference, the recipes in the front of the book that are in 1.5” high pans are Rose Factor 3.