How to prevent timestamp of published resources to be modified

I put the images for my site in assets/images/. During site generation, I use the Fit method to create a downscaled version of each image. The downsized images are displayed on the pages and link to the original. The shortcode code is like this:

{{ with resources.Get $img  }}
   {{ with .Fit "756x756 webp" }}
      {{ $.Scratch.Set "srcSmall" .RelPermalink }}
   {{ end }}
   {{ $.Scratch.Set "srcLarge" .RelPermalink }}
{{ end }}

As both versions of the image are referenced with RelPermalink they get both published in public/images. The downsized image is published only once at the first site generation and keeps this timestamp on subsequent generation runs as long as the original is not modified. The original, however, gets published and its timestamp set to the current time at every site generation, even if it is not modified.

I use rclone for synchronisation with the web site. As it synchronizes based on file timestamps, all image originals get uploaded at each synchronisation because the local timestamp is always newer than on the site, even if the images are identical. As this concerns some hundreds of megabytes of images, I am looking for a way not to touch the local timestamp at each site generation. I can not use the solution proposed in this topic, i.e. to solve the problem during site synchronisation, as my web server does not support rsync nor any of the synchronisation methods provided by hugo deploy.

As a workaround, I do some dummy image processing on the originals, for example converting from jpg to webp without resizing. This work fine but seems not very smart. And it would not work for files other than images.