Nginx throwing 404 for request, instead of performing try_files - nginx

Question

I have the following block in my nginx configuration file:
location /cat {
try_files $uri $uri/ /index.php?url=$uri;
}
When I try any of the following URLs, this works as expected:
http://example.com/cat/test
http://example.com/cat/test/test
http://example.com/cat/t
The following, however, do not. Instead of a redirect, I get a 404 error.
http://example.com/cat/test/
http://example.com/cat/test/test/
http://example.com/cat/t/
I'm not very experienced with nginx, so let me know what further information might be needed. This has me quite stumped.
Edit: I did come across this, but I would prefer to avoid using rewrite (for the sake of efficiency), plus this seems like an unnecessary band-aid:
https://serverfault.com/questions/755646/nginx-use-try-files-to-serve-file-instead-of-directory
Edit 2: Here is the full config
server {
listen 64.40.99.86:80;
server_name example.com;
server_name www.example.com;
client_max_body_size 128m;
root "/var/www/vhosts/example.com/httpdocs";
access_log "/var/www/vhosts/system/example.com/logs/proxy_access_log";
error_log "/var/www/vhosts/system/example.com/logs/proxy_error_log";
if ($host ~* ^example.com$) {
rewrite ^(.*)$ http://www.example.com$1 permanent;
}
location / {
proxy_pass http://64.40.99.86:7080;
proxy_set_header Host $host;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header X-Accel-Internal /internal-nginx-static-location;
access_log off;
}
location /internal-nginx-static-location/ {
alias /var/www/vhosts/example.com/httpdocs/;
add_header X-Powered-By PleskLin;
internal;
}
location ~ ^/~(.+?)(/.*?\.php)(/.*)?$ {
alias /var/www/vhosts/example.com/web_users/$1/$2;
fastcgi_split_path_info ^((?U).+\.php)(/?.+)$;
fastcgi_param PATH_INFO $fastcgi_path_info;
fastcgi_pass "unix:///var/www/vhosts/system/example.com/php-fpm.sock";
include /etc/nginx/fastcgi.conf;
}
location ~ ^/~(.+?)(/.*)?$ {
proxy_pass http://64.40.99.86:7080;
proxy_set_header Host $host;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header X-Accel-Internal /internal-nginx-static-location;
access_log off;
}
location ~ \.php(/.*)?$ {
fastcgi_split_path_info ^((?U).+\.php)(/?.+)$;
fastcgi_param PATH_INFO $fastcgi_path_info;
fastcgi_pass "unix:///var/www/vhosts/system/example.com/php-fpm.sock";
include /etc/nginx/fastcgi.conf;
}
location ~ /$ {
index index.html index.cgi index.pl index.php index.xhtml index.htm index.shtml;
}
location /cat {
try_files $uri $uri/ /index.php?url=$uri;
}
}