Do you get any errors during the provisioning concerning drivers? It could be the driver is not digitally signed, and that could prevent Windows from installing it.
We also use HII and have a batch file that executes all the required driver setup files, silently. Each driver is tested for each model, then stored on a share. As part of provisioning, the template will copy a utility to determine what machine type, and also a batch file to determine what drivers are needed, based off of the results of the machine type script. Then it will copy the setups to the local temp folder, run them all, and then delete the temp folder. After the next reboot, the drivers are installed and configured, and are ready to go.