You may want to think about buying
this then...

("for the hall")
On the other hand,
this will be a nicer (more portable) alternative.
If I did what you've done (off with the keyless entry) doesn't the keyfob still give out waves of interesting vibes to unscrupulous scrotes? If not, does one just use it in the same way as an ordinary lock/unlock jobby with the buttons as with an older car? I could live with that to avoid the constant looking-over-the-shoulder for no-gooders.
Re the above, second item, perhaps cutting a sliver of bacofoil to trap in the gusset seal would make it 100% if it's not already (I haven't bought one yet) though if you read back a few messages I did get a pouch, put my wife's Captur key card and my 500X fob in there and got into both cars no problem.
I have also looked at the steering wheel lock devices and checked online to see what is recommended - it's the Disklok every time but what a monster to mess with - though having a car with one to mess with is better than no car at all. The device which clamps to the wheel and rests on the dash looks good and is very visual.
I often thought that a 120dB horn in the car would stop any tosser lasting more than a few seconds inside a cab but how to wire it to save my own hearing is a bit out of my reach at the moment. It's a pita to find that the 500X with all its gadgets doesn't have an alarm (or does it, beyond deadlocking if Fiat think that's enough?)
R-V-M
Just in discussion - if I'm using the fob to gain entry or lock up, I'm still using a broadcasting signal so isn't that still receiveable by some low-life with the gizmo for doing what it does?
Wrapping the key fob in aluminium foil stops the keyless entry working in my car. There must be a market now for a neat hinged aluminium box for the hall to put your fob in. Very important that the door is properly sealed electrically, with some kind of conductive gasket.
Although I don't think there is too much demand for stolen to order 500X's, I've switched my keyless entry off in the menu, having watched CCTV footage today on the BBC website of a Merc being stolen using an rf signal booster. Official police advice - fit a Thatcham approved steering wheel lock. Back to the good old 70s when you had to fit a Krooklock to avoid your Cortina being nicked! Still doesn't prevent them pinching stuff from your car.
It's a disgrace that manufacturers have fitted such insecure gadgets to our cars. I wonder if the Merc owner who has CCTV evidence has a case against Mercedes for providing a security system not fit for purpose? Could be rich pickings for the ambulance chasers here!