A long time ago I put my Snapper Card (NZ equivalent) in a cup of acetone to get the chip out. I then stuck the chip in the back of my Nokia bar phone.
So while possible unfortunately tampering with Oyster cards is frowned upon by TfL. It might not technically be illegal but it'll certainly run you into problems when checked by traffic inspectors.
The answer to this StackExchange question gives an in-depth explanation of the Oyster card's cryptographic architecture, which shows that the card being as tamper-proof as possible is very much by design:
I would suspect that your troubles go beyond "frowns". A ticket inspector wants to see a valid oyster card, not a party trick, and whether it scans or not, I don't think it's a high bar to argue that a tampered with card isn't valid, period.
(Officially, at least. I've seen them happily scan the outsides of people's wallets.)
> 5.1 All photocards and Oyster photocards remain our property and must not be intentionally
damaged, altered or tampered with in any way. We may withdraw or cancel your photocard or
Oyster photocard at any time
> (1) No person shall alter any ticket in any way with the intent that an Operator shall be defrauded or prejudiced.
> (2) No person shall knowingly use any ticket
which has been altered in any way in breach of Byelaw 20(1).
Which makes it sound like this tampering would be okay, but they also say this:
> (1) In any area not designated as a compulsory ticket area, no person shall enter any train for the purpose of travelling on the railway unless he has with him a valid ticket entitling him to travel.
> (2) A person shall hand over his ticket for inspection and verification of validity when asked to do so by an authorised person.
...and it's likely TfL won't see these as valid tickets.
> having the apparently unqualified right to cancel the card
Is unfortunately required to handle the various con artists and scammers who would exploit loopholes the TOS.
Yes, I believe you can be in the wrong while following the letter of the law; that's part of the reason why we have so many damned laws: to close loopholes exploited by assholes.
Of course some asshole in the system can abuse that clause right back, but that's the cost of doing business with people on both sides.
And it being a public service, they generally can't deny you the use of it (at least not 'unqualified', I'm sure there could be some sort of police or court order taken out against people) - but they can specify exactly how you're going to pay for the service.
Also, I'm pretty sure "cancelling" means "forced reissue", not forfeiture of a legitimate ticket or balance.
RingTheory makes rings that can access the MBTA (mass transit) in Boston. The product is the "Sesame Ring" and they have partnered with the MBTA on this.
http://www.ringtheory.com/#home
This makes me wonder, could you make/3d print a simple ring for your finger and pop your oyster card (uk) / suica card (jp) / t money card (korea) / etc in it? It would essentially be just as seamless as an embedded chip in your hand, without the messiness.