Yep - technical skills (other than IT which is my profession) are going to need to roll on in. For now - to keep things easy - do I simply get a freewheel 13 toothed cog which sits on the existing hub - then flip the rear wheel around?
You won't be able to find a 13t freewheel, You can with a fixed sprocket, but a freewheel mechanism inside the freewheel restricts the size it can be.
Be aware that BMX sprockets can be smaller, but I think that the hub thread size is also smaller.
To get the right size, assume that your wheel is 27" in diameter, then multiply by the number of teeth on the chainwheel and divide by the number on the rear sprocket. If the result is greater than 70, then you are going to have hard time on any incline.
Good luck - as an IT person, you should be Agile.