Continental tyres "welded" to rims!

Easy to get off, get a pair of pipe grips, nip tyre just above rim, squeeze. This will break any bond has to rim, repeat around wheel

I have some of these in 25's on my winter bike & they are a pig to get on & off. Hoping I wouldn't have to do it that much as they are supposed to be hard to puncture. Only had 1 so far & it took me a lot longer than it should, not what you want at the roadside.

Although after I slid out & came off yesterday might be looking for something with considerably more grip......... 

changed some today for a customer.... hateful tyre...   I find you need to squeeze the bead around the rim to unhook it.... then using plastic levers (I use the wide B'twin ones on these tyres and Marathon/Plus) you can ease under the bead and the job is done...

How about clamping both sides of the tyre with a set of mole grips as close to the rim as you can and then pulling the mole grips back over one side of the rim? That should unseat the bead on the opposite side.

The thick plastic levers from the LBS do jobs okay here. Plastic against rims yet although thick the initial bite into the bead is sharp and angled. Hence should get in without damaging. Contoured cross section interlocks them when not in use and provides strength when used as a lever.
I bought 2 sets; different brands yet same priority to use, both cost about $5 per 3.

I've had similar at the roadside, the issue is you need to get the bead into the channel which runs around the middle of the rim.

I had some GP4000sii which wouldn't unseat from the hook, so I couldn't move them to the centre channel.  In the end it took two men and park tools tyre lever with a much thinner end than my levers to unseat the bead from the hook.

At home, a screwdriver, wrapped in a old t-shirt would likely do the trick without damaging the rim.