Why would momentum not be conserved if the particle and wave were co-directional?

Here some facts wich give you the answers :

In 1924, Luis de Broglie  (Nobel Prize in Physics in 1929) proposed that a wave function is associated with all particles.  Where this wave function has nonzero amplitude, we are likely to find the particle.  The standard interpretation is that the intensity of the wave function of a particle at any point is proportional to the probability of finding the particle at that point.  The wavelengths of the harmonic waves used to build the wave function let us calculate the most likely momentum of the particle and the uncertainty in the momentum.  The wave function for a material particle is often called a matter wave.

The relationship between momentum and wavelength for matter waves is given by p = h/λ, and the relationship energy and frequency is E = hf.  The wavelength λ = h/p is called the de Broglie wavelength, and the relations λ = h/p and f = E/h are called the de Broglie relations.  These are the same relations we have for the photon, but for particle E = (1/2)mv2 = p2/(2m), so E = ћ2k2/(2m), λ = h/√(2mE).  The relationship between λ and E is different for particles than for photons.

A spread in wavelengths means an uncertainty in the momentum. The uncertainty principle also holds for material particles. The minimum value for the product ∆x ∆p is on the order of ħ.

∆x∆p ~ ħ.

For any particle, we cannot predict its position and momentum with absolute certainty. The product of the uncertainties is on the order of h/2π = ħ or greater.

A free particle of mass m moving with exactly determined velocity v in the positive x-direction has momentum p = mv, pointing into the positive x-direction and kinetic energy E = p2/(2m).  Its wave function, which often is denoted by ψ(x,t),  is a plane wave. 

ψ(x,t) = Acos(kx - ωt + φ)

[The wave function is actually a complex function, and Acos(kx - ωt + φ) is the real part of this function.  We will learn about complex functions in the next section.]

The wave function has a well defined deBroglie wavelength λ = h/p which determines k = 2π/λ. 

The wave function also has a well defined deBroglie frequency f = E/h, which determines the angular frequency ω = 2πf.

As you notice this is not a real quatum field theories point of view, but is what majority of people use. The first paragraphe tell you that the particle and wave go in the same direction and sens. if not you'll get probability equal zero. I leave it as exercice for the reader to find the answers wich are very clear here.

one additional point:

matter wave is a wave of probability contrary to electric or magnetic field, it does not carry an energy, only density of probability. this  the subtility resolved by quantum field theory. Because we don't have  a fermionic wave in classical regime. we introduced the wave of probability so we can treat a bosoic and fermionic wave identically using schrodinger equation. people talking about second quantization, in fact there is always one quantization, but we start this time from wave of probability.