As far as I know there is no way of manually organising the album thumbnails. Even if there was when you add a new album you would have to move that, to keep it in the position you want.
An easier way would be to make an album of albums, organise the albums the way you want. When that album has been uploaded edit your profile page and enter the url for the album of albums in the ‘site’ field. Users can the go to your profile page and click on your site link, for family/friends just email the link to the master album.
https://jalbum.net/help/en/Making_an_album_of_albums_with_web_locations
Failing that you would need to ask for a website feature request to allow manual sorting of albums. I think it has been asked for before, so not sure it would be possible.
