What's the best way to leave an air flow shaft in wood chips after removing a PVC pipe?
If I understand the setup, the goal of the PVC is to keep the pile aerated so it will be aerobic composting.

Some alternative solutions:


Figure out a way to periodically turn the pile and keep it fluffed-up. Turning the pile has multiple benefits beyond just aerating the pile. It also helps spread the beneficial bacteria. It also moves material from the dryer and colder edges/tops into the damper and hotter middle of the pile where it will be composted.
Get some more pipe. If cost or environmental impact are issues you could try to get some used or discarded pipes. One good trick is to set up an email alert from craigslist. You can also often find good materials at a used building goods store (in some cities these are run by Habitat for Humanity or similar organizations).
Use other materials in the pile to create a structure that has air pockets, like longer branches or stalks from plants like sunflower stems or corn stalks. These materials might not all compost as quickly as the wood chips and would need therefore need to be filtered out at the end to be composted twice. However, they should hopefully help the wood chips to compost.