If I remember correctly, my Picture Resizer also keeps the metadata intact when rotating.
Maybe the best solution for you would be to not rotate the images at all and let the online system do the job in the future? If you do not have access to the original pictures and need to deal with a large amount of images with wrong rotation tags, you need something to overwrite them. RealWorld Photos with the right scripted batch operation should be able to do it, but it is a paid program, maybe you can find a free solution somewhere on the web.