A better option though would be to Go Around from Base Leg onto the Dead Side and join again.
if you had just said 'Go Around from Base' that would make sense but to then say go "onto the Dead Side and join again" is, in my opinion, really asking for trouble as you are leaving the circuit from a very unusual position and will likely conflict with other (eg Joining) traffic.
Level Attitude, sorry beg to disagree with you here! An aircraft flying a straight in is not conforming with the pattern formed by other aircraft.
Yes it is.
Conforming with the pattern means flying over (roughly) the same track, at (roughly) the same height and in the same direction as other aircraft.
It does not mean the whole pattern has to be flown and it states nothing about priority or giving way.
An aircraft joining Straight In will fly the same last portion of the final approach track as all other aircraft so once they are 'Final' they have right of way to land.
I do agree this is confusing at uncontrolled airfields where different joins can be used but, unless anyone can reference where it says that Final traffic, in certain circumstances, must give way to circuit traffic then ' Them is the Rules'