HAProxy over Tomcat returns Error 403

I have an old server which runs a Tomcat service on port 8080. For various reasons (including securing the access from clients) I had to set up a HAProxy server in front of it, secured with a SSL cert.

This is the HAProxy relevant config:

frontend myservice
    mode    tcp
    option  tcplog
    option  logasap
    log     global
    option  tcpka
    bind    10.10.10.10:80
    bind    10.10.10.10:443 ssl crt /etc/ssl/haproxy/myservice.example.org.pem
    acl secure dst_port eq 443
    http-response add-header Strict-Transport-Security "max-age=31536000; includeSubDomains; preload;"
    http-response replace-header Set-Cookie (.*) \1;\ Secure if secure
    use_backend bck_myservice if { hdr(Host) -i myservice.example.org myservice }
    default_backend bck_deny

backend bck_myservice
    mode     tcp
    balance  leastconn
    option   prefer-last-server
    server   oldserver.example.org oldserver.example.org:8080 weight 1 check port 8080 inter 2000 rise 2 fall 5 ssl verify none

backend bck_deny
    mode http
    http-request deny

10.10.10.10 is the VIP of the new service, mapped to myservice.example.org.

Accessing http://oldserver.example.org:8080 works fine as usual.

The problem: https://myservice.example.org results in an error "403 Forbidden". Accessing that URL does not seem to hit the Tomcat backend, as there is no trace of it in the Tomcat logs. (Note: the HAProxy config used to have mode http but it resulted in an error "503 Service Unavailable".)