My name is Eduard, I will help to solve your problem. I inspected the ST module and found the following: there are 5 functions related to fetch the strings and their translations, but exactly the one you mention misses the per request cache.
Answers to your questions:
1) Yes, it is a known issue, but it was scheduled to fix later as not top priority.
2) Caching is already enabled in other functions that fetches strings and translations(that are used in most of the cases). There is no setting currently to enable it in this specific function.
3) Yes, I can update it, test and install updated ST version on your server, I just need an access to server in that case. As an alternative I can just provide a package and you will install it.
We will also include that fix in the next ST version release.
4) Confirming, the cache is required on the WPML side. I can add it, it is very simple.
About temporary workaround: it will not work, but as I mentioned in point 3 the fix in ST module is very simple, so we can implement it ASAP. Please provide the way you want us to process this. If you want us to install and test it, I will create special secure form(it will visible only by WPML support), where you can share credentials.
