There's no weird sensors in the A4 rims/wheels etc that would be interfered by external Tyre pressure monitoring caps is there?
Eg http://www.tyredog.co.nz/4-wheel-wtpms/4-wheel-tyre-pressure-monitor-0-to-60-psi.html
or
https://www.trademe.co.nz/motors/car-parts-accessories/other-accessories/auction-1488068123.htm
Check out Fobo.
I have them on my motorbike and they are great.
https://my-fobo.com/Product/FOBOTIRE (https://my-fobo.com/Product/FOBOTIRE)