I live on top of a substantial hill .... i have a heart condition and an implanted device .... i can ride for miles .. but climbing hills is not good for me .. So i drive to the bottom of the hill, cycle, then drive back up the hill ..........
Exercise is essential for my health, swimming pools are closed, i have to avoid impact exercise ... so cycling it is ...
You have made a case for ignoring the 'exercise must begin at home' restriction, but not a valid one.
Walking is not an impact exercise.
You can get all the essential exercise you need by walking from home, so you have no essential need to cycle.
I have limited sympathy with the argument that only driving half a mile up and down a hill is not a massive breach of the restrictions.
It is still a breach, and could have a negative impact in that people may see you doing it, which undermines the compliance of others.
Mention of seeing bikes on a car roof has been made in this thread.
You do have the option of getting all the essential exercise you need and fully complying with the restrictions.
That is the option you should take.