It works for the original dataset pretty well. Here's what comes out:

> summary(model1 <- lmer(score ~ nstates_amp_and_freq_n:phase_order:phase +
+                    (1 | id) , data=all, REML=F))
fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
Linear mixed model fit by maximum likelihood  
t-tests use  Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula: score ~ nstates_amp_and_freq_n:phase_order:phase + (1 | id)
   Data: all

AIC BIC logLik deviance df.resid 
 -12.3 5.3 14.1 -28.3 58

Scaled residuals: 
 Min 1Q Median 3Q Max 
-2.1345 -0.7098 -0.1321 0.7379 1.9288

Random effects:
 Groups Name Variance Std.Dev.
 id (Intercept) 0.01448 0.1203 
 Residual 0.02791 0.1671 
Number of obs: 66, groups: id, 22

Fixed effects:
 Estimate Std. Error df t value Pr(>|t|) 
(Intercept) 6.402e-01 3.506e-02 2.606e+01 18.260 2.22e-16 ***
nstates_amp_and_freq_n:phase_order0:phase0 7.747e-02 3.836e-02 5.587e+01 2.020 0.048236 * 
nstates_amp_and_freq_n:phase_order1:phase1 1.934e-01 8.274e-02 6.110e+01 2.338 0.022698 * 
nstates_amp_and_freq_n:phase_order2:phase1 5.329e-02 6.533e-02 6.363e+01 0.816 0.417712 
nstates_amp_and_freq_n:phase_order1:phase2 8.565e-04 4.749e-02 6.113e+01 0.018 0.985668 
nstates_amp_and_freq_n:phase_order2:phase2 2.412e-01 6.279e-02 5.894e+01 3.842 0.000301 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
 (Intr) n____:_0 n____:_1:1 n____:_2:1 n____:_1:2
ns____:_0:0 0.255 
ns____:_1:1 -0.044 0.021 
ns____:_2:1 -0.011 0.114 0.005 
ns____:_1:2 -0.148 0.033 0.009 0.190 
ns____:_2:2 -0.207 -0.112 0.161 -0.005 0.026 
fit warnings:
fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
 

Here are the coefficients represented graphically:

Note how the two conditions behave in markedly different ways. The lower coefficients (which is the second condition) indicate the second condition allows better compression than the first condition. The first condition shows a gradual increase in the number of states (although the increase from 2 to 3 is not significant), whereas the second shows an immediate and significant decrease in the number of states, followed by a non-significant increase.

Finally, \(R^2 = 0.6159172\).