My belief is that a long bar (i.e. the distance between the hinge pin to the breech) is more important that the 3rd grip. It is hard to find a shotgun action with a long bar, as it is heavier than a short one, and not really necessary on a shotgun.
It is no coincidence that most Webley rifle were built on their long bar action.
All my shotguns have a bar shorter than 2", while all my double rifles have a bar longer than 2". Fluke? I think not...
IMHO, a long bar gives more leverage to the bolts as well as a reduced "deflection" angle (the angle between the bore center line and the line from the firing pin to the hinge pin. Both of these will reduce strain to the Purdey bolt and/or the 3rd grip, whatever it is.
The idea of the 3rd grip is to reattach the barrel to the top of the action, which goes in the right direction as well, assuming that it is well done. I think that the problem with the 3rd grip is that it is mighty hard to have an effective one, as the adjustments involved are difficult.
A long bar also reduces the sideways strain due to the excentricity of the left and right barrels. This aspect is mitigated by a doll's head and/or sideclips which help reduce lateral motions. The reason is that a longer bar usually implies a longer lump, which helps in absorbing the lateral torque.

It must be said that a rifle built on a short bar action or without a 3rd bite will probably survive. The question is: how long?
The more margin to start with, the better off we are...

To sum it up, I think that:
- a longer bar is better
- a bar with minimum internal cutouts is better (such as back-action sidelock). Side bolsters also help.
- the less slop to begin with, the better
- a 3rd grip is fine but not absolutely necessary
- ditto for sideclips

Long bar shotgun actions are found on Greener Empire (*not Facile princeps*), some German guns, and some older guns as well as some of the cheaper guns.

Shotguns and rifles were built on different actions for good reasons, hence finding a suitable shotgun action to build a rifle is not easy!

WC