There is no reason to hold like the Rama unlike the Rambam.
I attend shuls where the sefer torah is handed to a woman to carry through the women’s section, which I find to be more appropriate than the male chazzan carrying it through the ezras nashim (they do this at the Carlebach Shul) or women not having the opportunity to kiss the sefer torah at all, which is just sad.
And, the above is correct. Megillah 23b says explicitly that where there is no issue of kavod hatzibur, women can have aliyos and lein. R’ Daniel Sperber, a great poseq and gadol betorah, is the poseq for Darkhei Noam Minyan on the Upper West Side, where women lein and have aliyos. Granted, other members of my hashqafic sphere aren’t crazy about this (like R’ Saul Berman and R’ Shlomo Riskin), but nonetheless, lo rainu eino ra’ayah.