For the free strongest lines, I obtained q values of -0.5, -0.4, and 0.2. The negative q's tend to increase u0 while the positive one decreases u0. In all cases, when q is free, taustar decreases, but keeps roughly the same confidence range.
fixed q
free q
O VIII: 18.9689
q=0
taustar=0.249 +/- (0.139:0.389)
u0=0.562 +/- (0.532:0.587)
norm=7.41e-4 +/- (7.12e-4:7.83e-4)

rejection probability = 96% (C=131.22; N=106)
O VIII: 18.9689

q=-0.518 +/- (-0.613:-0.372)
taustar=0.199 +/- (0.0938:0.335)
u0=0.672 +/- (0.620:0.710)
norm=7.49e-4 +/- (7.20e-4:7.92e-4)

rejection probability = 86% (C=122.35; N=106)
Fe XVII: 15.014

q=0
taustar=6.36e-2 +/- (0:0.165)
u0=0.562 +/- (0.525:0.583)
norm=2.07e-4 +/- (2.0e-4:2.26e-4)

rejection probability = 57.2% (C=233.18; N=266)
Fe XVII: 15.014

q=-0.434 +/- (-0.598:-0.285)
taustar=1.81e-2 +/- (0:0.120)
u0=0.637 +/- (0.564:0.693)
norm=2.15e-4 +/- (2.03e-4:2.37e-4)

rejection probability = 3% (C=231.29; N=266)
Ne X: 12.1339

q=0
taustar=0.591 +/- (0.372:0.858)
u0=0.651 +/- (0.609:0.692)
norm=7.59e-5 +/- (7.11e-5:7.97e-5)

rejection probability = 36.40% (C=179.93; N=184)
Ne X: 12.1339

q=0.204 +/- (-0.110:0.802)
taustar=0.544 +/- (0.346:0.808)
u0=0.613 +/- (0.536:0.686)
norm=7.51e-5 +/- (7.1e-5:7.9e-5)

rejection probability = 38% (C=179.52; N=184)
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