Control when session starts/stops

Hello,

My provider has a buggy varnish config setup that I am trying to work around. To do so, I would like control when a session starts and stops. More precisely, I would like to be able to control when the _wp_session cookie gets created and I would like it to get removed when necessary.

The scenario would be as follows:
1) Visitor loads site. Session is not created yet, cookie is not set.
2) Visitor adds product to store cart. Session starts, cookie is set.
3) Cart gets emptied (visited removes all products from cart or after checkout). Session stops, cookie is unset.

Is there a clean way to do this without hacking the plugin too much? is it a bad idea to try to do this? (versus get my provider to fix their varnish cache support)

I am using the plugin to create a cart session timer and it works great. A timer starts counting down once something added to the cart. Once the timer expires, the cart is automatically emptied. A la ticketmaster.