I don't know csh but I have a similar requirement for ksh. My hack solution was to
eval source <(ksh -c ". /path/to/my_script.kshenv|sort)
I ran into issues with quoting and ended up putting in some grep patterns after the env to remove environment variables that I didn't want carried over but it kinda worked.
I found another useful bit here:
https://www.theunixschool.com/2010/07/how-to-access-child-shell-env-variable.html
This little bit of sed creates properly quoted export commands:
sed 's/^/export /;s/=/=\"/;s/$/\"/'