lonhig, you can absolutely do what you want.
Move your location /logs/ directive before try_files. Also, remove the trailing slash for logs and add the URI to the pass:
location ~* /logs {
proxy_pass http://192.168.0.105:8000;
}
The tilde + asterisk will make the match case-insensitive. Remember, Nginx removes the matching portion in the handoff, so if you the URL for Kibana is 192.168.0.105:8000/logs/, you will have to add it back in on the pass:
location ~* /logs {
proxy_pass http://192.168.0.105:8000/logs/;
}