Lots of brands include white dresses that would be bridal appropriate - it's not too late to get something you like! So if the SP dress doesn't suit you, then loads of that type of brand do stunning dresses in white that don't cost 4 figures. Hope you get something you love and feel good in. Rixo and Reformation may feel too casual to you if you worried SP was too youthful, but there is so much if you just e.g. look at white party dresses on Net a Porter.
Edited to add: Oh I see you saw SP on NAP! So you're all over this. I always wonder who is wearing those white dresses as they feel so bridal to me.