We followed Geoff's advice with the silicone cup (lid actually) and filled our Suunto with Johnson's baby oil. Half a year later, this seems to have worked apart from having a small bubble at the top, as there must've been some air trapped under the disc. Should be sorted with a top-up.
A hairdryer will help with getting the very tight bottom off. Matches all around for the small plastic clips at the top of the globe.