How would gyroscopic effects affect push-pull configuration vs conventional twin engine in the event of engine failure?
Gyro precession effects from a propeller are minimal when at flying speed and making modest pitch and yaw motions, where the precession is mild and there is lots of aerodynamic damping.  You don't really notice it. Propeller slipstream over the rudder has a much bigger effect, which a lot of people may confuse with precession. 

You have to make large sudden pitch or yaw motions at low speed, like when taking off a taildragger with a very large propeller. If you raise the tail suddenly at low speed, precession of the propeller will make the airplane swing noticeably.  Or, with aerobatic airplanes that make extreme pitch and yaw motions and where precession will have an effect that has to be taken into account (as well as putting massive stresses on the crank at the prop flange).

For wing mounted engine twins, the effects of offset thrust are the main limitation, with a minimum control speed that is usually well above the stall and below which the airplane will roll over.  Centerline thrust aircraft avoid this problem for obvious reasons.  In any case, I don't believe gyro precession is a factor at all in a Cessna 337, on either engine, or on a regular twin for that matter because the pitch and yaw rates you generate aren't enough to create significant precession effects that could affect controlability.

In the end though, with piston twins, gyro precession is the least of your problems.  The biggest one is the fact that the loss of 50% of thrust leaves you with almost no performance reserve.  Wing mounted engines leave you with a somewhat more dangerous situation due to the ability to lose complete control well above the stall by dropping below minimum control speed, but even with center line thrust, the single engine performance is so marginal that if you are at gross weight and above sea level and it's hot, you are going down anyway. Yes there is no Vmc limit, but you are still faced with having to maintain minimum speed for performance and chances are you are still going to crash land eventually and you may ending up stalling and spinning it the regular way if you panic trying to will the plane to fly, just like a regular twin.

For this reason I don't believe center line thrust aircraft have all that much better a safety record following engine failures than regular twins.