Limit options when creating content according to selected value
I got this sorted (eventually...)

Rather than having Discipline as a content type (since it was only really storing the name) I created a taxonomy vocabulary called Discipline and added all the relevant discipline names as terms. 

Removed the entity references to Discipline in Event and Championship. Added a term reference (field_discipline) to Event and the same term reference to Championship. 

Using the Reference Option Limit module (and patch; see question) in the entity reference in Event to Championship added the 'Limit this field's options according to matching field values' and selected the matching field field_discipline.

So now when creating an Event node the user is presented with a list of checkboxes to select the discipline(s) involved and when each is selected the appropriate championships are added to the list of available championships.