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EDIT: It turns out that the issue was not in the MATLAB to SPICE porting but rather in the original MATALB script itself. The MATLAB/Python script did not use a the same timestep as the real simulation.
I measured the experimental timestep and found it to be dt~=0.08s, so by using Euler with dt=1/10000 the MATLAB script was effectively simulating for only 60 ms, instead of the 50 s in the real experiment. Scaling the Ap and An parameters to match the updated - much larger - timestep was enough to reproduce the experimental results.

I have been attempting to port a modified version of the Yakopcic memristor from Python/MATLAB to LTspice but have been running into issues with the results not being the same. In Python/MATLAB the memristor is simulated by using Euler's method to solve the IVP describing the device's internal state evolution.

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I think that this answer may have put me on the right track (https://electronics.stackexchange.com/a/368910/294242) by pointing out that timing in the SPICE engine could lead to issues.
In fact, if I enlarge my timestep from dt=1/10000 to dt=1 in MATLAB/Python, I get the same exact result as in LTspice.

Is there any way to solve the issue I'm seeing? I have tried .tran 0 50s 0 {1/10000} to match dt=1/10000, but the results don't change.

I have been attempting to port a modified version of the Yakopcic memristor from Python/MATLAB to LTspice but have been running into issues with the results not being the same, as shown in the following pictures. 
In Python/MATLAB the memristor is simulated by using Euler's method to solve the IVP describing the device's internal state evolution. 

MATLAB simulation result
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LTspice simulation result  

I think that this answer may have put me on the right track (https://electronics.stackexchange.com/a/368910/294242) by pointing out that timing in the SPICE engine could lead to issues.
In fact, if I enlarge my timestep from dt=1/10000 to dt=1 in MATLAB/Python, I get the same exact result as in LTspice.

MATLAB simulation with dt=1 (the curve in black)

Is there any way to solve the issue I'm seeing? I have tried .tran 0 50s 0 {1/10000} to match dt=1/10000, but the results don't change.

Is there any way to solve the issue I'm seeing? I have tried setting tmax in the .tran command to 100u to match dt=1/10000, but the results don't change.

Is there any way to solve the issue I'm seeing? I have tried .tran 0 50s 0 {1/10000} to match dt=1/10000, but the results don't change.

* SPICE model for memristive devices
* Created by Chris Yakopcic 
* Last Update: 8/9/2011
*
* Connections:
* TE - top electrode
* BE - bottom electrode
* XSV - External connection to plot state variable
* that is not used otherwise

.subckt MEM_YAKOPCIC TE BE XSV

* Fitting parameters to model different devices
* gmax_p, bmax_p, gmax_n, bmax_n:      Parameters for OFF state IV relationship
* gmin_p, bmin_p, gmin_n, bmin_n:      Parameters for OFF state IV relationship
* Vp, Vn:                              Pos. and neg. voltage thresholds
* Ap, An:                              Multiplier for SV motion intensity
* xp, xn:                              Points where SV motion is reduced
* alphap, alphan:                      Rate at which SV motion decays
* xo:                                  Initial value of SV
* eta:                                 SV direction relative to voltage

.param gmax_p=9e-5 bmax_p=4.96 gmax_n=1.7e-4 bmax_n=3.23 
+      gmin_p=1.5e-5 bmin_p=6.91 gmin_n=4.4e-7 bmin_n=2.6 
+      Ap=90 An=10 
+      Vp=0.5 Vn=0.5 
+      xp=0.1 xn=0.242 
+      alphap=1 alphan=1 
+      xo=0 eta=1


* Multiplicative functions to ensure zero state
* variable motion at memristor boundaries
.func wp(V) = xp/(1-xp) - V/(1-xp) + 1
.func wn(V) = V/xn

* Function G(V(t)) - Describes the device threshold
.func G(V) = 
+    IF(V > Vp, 
+        Ap*(exp(V)-exp(Vp)), 
+        IF(V < -Vn, 
+            -An*(exp(-V)-exp(Vn)), 
+            0 ) )

* Function F(V(t),x(t)) - Describes the SV motion 
.func F(V1,V2) = 
+    IF(eta*V1 >= 0, 
+        IF(V2 >= xp, 
+            exp(-alphap*(V2-xp))*wp(V2), 
+            1 ), 
+        IF(V2 <= xn, 
+            exp(alphan*(V2-xn))*wn(V2), 
+            1 ) )

* IV Response - Hyperbolic sine due to MIM structure
.func IVRel(V1,V2) = 
+    IF(V1 >= 0, 
+       gmax_p*sinh(bmax_p*V1)*V2 + gmin_p*sinh(bmin_p*V1)*(1-V2), 
+       gmax_n*sinh(bmax_n*V1)*V2 + gmin_n*sinh(bmin_n*V1)*(1-V2) 
+       )

* Circuit to determine state variable
* dx/dt = F(V(t),x(t))*G(V(t))
Cx XSV 0 {1}
.ic V(XSV) = xo
Gx 0 XSV value={eta*F(V(TE,BE),V(XSV,0))*G(V(TE,BE))}
* Current source for memristor IV response
Gm TE BE value = {IVRel(V(TE,BE),V(XSV,0))}

.ends MEM_YAKOPCIC