Why does entanglement not imply hidden variables? By the causal symmetry of spacelike-seperated events, the statement "measurement of particle 1 causes subsequent collapse for particle 2" is equivalent to "measurement of particle 2 causes subsequent collapse for particle 1". With the ordering of the random wave-function collapse happening both ways, surely the randomness is logically rendered non-existent? [Like $A\implies B$ and $B\implies A$ is logically equivalent to $A\equiv B$] Implying a situation where the outcome is predetermined by extra hidden variables.  presumably there is a way out for orthodox QM? 
 A: 
By the causal symmetry of spacelike-seperated events, the statement "measurement of particle 1 causes subsequent collapse for particle 2" 

This is a wrong statement, I guess from the bad terminology of "collapse". Nothing collapses with a measurement, the wavefunction is not a balloon to collapse. When complex conjugate squared gives  a probability distribution for the system under study. It is one "throw of the dice" in building up the probability density distribution.
The well known double slit experiment shows clearly the role of a "measurement", collapse in your language, to the probability distribution that the wavefunction of the system predicts.

Each individual measurement builds up the probability density distribution experimentally showing the interference pattern , the wave nature of probability.

is equivalent to "measurement of particle 2 causes subsequent collapse for particle 1".

The mistake here is in thinking that there are two wavefunctions , in your terminology. There is one unique wavefunction describing quantum mechanicaly the probabilities for a given system. One mathematical solutions with the given boundary conditions. When one "measures" , that's it, a new wavefunction has to describe the two particles, if they are still quantum mechanically connected and have not decohered, i.e. lost the phases that make it a wavefunction.
For example the dot that is the electron is a summed path of the various new scatters of the electron after it hits the screen, the wave function of "electron +double slit" has "collapsed", in your language.

With the ordering of the random wave-function collapse happening both ways, surely the randomness is logically rendered non-existent?

There are no two ways, there is ONE wavefunction for both at a time A and B, if not, they are not in a quantum mechanical solution of the boundary conditions. A measurement is a measurement. If A is measured the state of B is known if the system is in a quantum mechanical state. The same with the coin, if heads are on top, tails are on bottom.
[Like A⟹B and B⟹A is logically equivalent to A≡B] 
In quantum mechanics A and B are conditions that hold at the same time in a wavefunction representation of a system.

Implying a situation where the outcome is predetermined by extra hidden variables.

Well, for the coin the extra hidden variable is that the two sides are glued together back to back.

presumably there is a way out for orthodox QM? 

the way out is that it is ONE quantum mechanical solution of the boundary value problem.
Your comment here :

I'm trying to say, albeit poorly, that if two independent (since they're causally disconnected) probabilistic events occur, that always turn out perfectly anti-correlated, surely there is a rigorous way of deducing that the probability distributions are trivial?

They are not  "causally disconnected'" in the case of quantum mechanical entities. All quantum mechanical equations follow causality, and the wavefunctions in all their aspects, if one knows the particular wavefunction as you state,  are like the two sides of a coin . What you name "collapse" is a "measurement" and a measurement is one point in a cumulative probability distribution as shown by the double slit single electron at a time, above.
