Haproxy: how to prepare a server maintenance without kicking app sessions

The issue

I'm using haproxy to load balance web servers. I use session persistence with additional cookies as some applications use session files and these are not synchronized between servers.

I want to disable a server for maintenance, but without breaking sessions. So I would like to allow existing clients to continue their application session, but not accept new clients.

haproxy behavior

• I set a server to "going to maintenance"
• if a client has the cookie set, use the server even if marked as "going into maintenance"
• if a new client (without cookie) come, it is directed to another server
• after all clients end their application sessions, no more client would have the cookie set to this particular server, and I'd be good to shut it down without user disruption.

Do you think this is achievable with some haproxy configuration?
Or is there a clever way to do it?

Other ways

Non exhaustive list of other ways to achieve this need:

• synchronize session files between servers (needs a way to synchronize files between several servers, or a common single mountpoint)
• use database to store session information (needs to change application behavior)

More details

I use this kind of configuration:

frontend https-in
   bind xxx.xxx.xxx.xxx:443 ssl crt /etc/haproxy/ssl/_default.pem crt /etc/haproxy/ssl
   reqadd X-Forwarded-Proto:\ https

   acl APP1 hdr(host) -i APP1.atac.local
   use_backend APP1 if APP1

   default_backend _default

backend APP1
   redirect scheme https if !{ ssl_fc }
   mode http
   balance roundrobin
   cookie HAPROXY_SESSION insert indirect
   option httpchk HEAD /haproxy_test_page.php HTTP/1.0\nUser-Agent:\ HAProxy
   server SRV1 SRV1_IP:PORT cookie SRV1 check
   server SRV2 SRV2_IP:PORT cookie SRV2 check

If I just disable SRV1 (with haproxy cli command), I think all application sessions opened on SRV1 will break after the end of the current HTTP "session". Is that right?