Struggling with nginx configuration with owncloud 10.0.4 in subdirectory

Try that:

change
root /var/www/owncloud/;
to
# root /var/www/owncloud/;
(you could actually also delete that line…)

change
fastcgi_split_path_info ^/owncloud(.+\.php)(/.*)$;
to
fastcgi_split_path_info ^(.+\.php)(/.*)$;

change
location ~ /owncloud(\/.*\.(?:css|js)) {
to
location ~ /owncloud(/.*\.(?:css|js)) {

change (this line is there twice - you need to change both occurences)
try_files $1 /owncloud/index.php$1$is_args$args;
to
try_files $uri /owncloud/index.php$uri$is_args$args;

restart nginx with nginx -s reload and navigate to https://192.168.xx.xx/owncloud

Sidenote: I noticed that you declare two lines as upstream php-handler. Although it sounds like in your setup nginx can communicate with php, I would only use one line (preferably a socket-connection). The socket-connection for php7.0-fpm in Debian Stretch should be unix:/run/php/php7.0-fpm.sock; instead of unix:/var/run/php7-fpm.sock;