SSH for loop: parameter passed to function captured in variable is not expanded

I have several servers which have several files with deploy date info I need to parse, and get a local copy of the files which are 2 months old or older.

#!/bin/bash

# split on new line not space
# don't want to quote everything
# globbing desired
IFS=$'\n'

servers=(
  blue
  red
)

parseDate() {
    grep 'deploy_date:' $file | \
    sed  ...                  | \
    # much more in here...
}

getOldFiles() {
    local #all vars
    currentDateInSecs=$(date +%s)
    twoMonthsInSecs=526000
    for server in ${servers[@]}; do
        oldfile=$(
          ssh $server "
            $(declare -f parseDate)
            for file in /dir/$server/file*; do
                dateInSecs=$(date -jf '%b/%e/%Y' $(parseDate) +%s)
                timeDiff=$((\$currentDateInSecs - \$dateInSecs))
                ((\$timeDiff >= \$twoMonthsInSecs)) &&
                    cat \$file
            done
          "
        )
        [ -n $oldFile ] &&
            cat $oldFile ~/oldFiles/${server}-${file}.txt
    done

### Problem: Current issue is with dateInSecs=$(date -jf '%b/%e/%Y' $(parseDate \$file) +%s). When parseDate \$file is in $() the $file variable is not expanded, it works fine without command substitution, but I need it. How do I fix this? ### Info: This isn't a script, they're in my ~/.bash_profile This is a script (among other scripts) in a git repo which is sourced from ~/bash_profile (I have an install script which sets sources using $PWD) so people can use these commands directly instead of cd'ing to the git repo (which has many other things not applicable to the them). Runs from Macos to CentOS servers.