I don't know how much it helps, but I think parametric survival models are
more robust if you want slopes
eg for your data above, a Weibull model:
survreg(formula = Surv(FailTime, Event) ~ x1 + x2 + (x1 + x2) *
frailty(cluster), data = x)
coef se(coef) se2 Chisq DF p
(Intercept) 7.47245 0.038162 0.030435 38340.62 1.0 0.0e+00
x1 -0.04780 0.047612 0.044369 1.01 1.0 3.2e-01
x2 0.06143 0.038344 0.038165 2.57 1.0 1.1e-01
frailty(cluster) 157.43 71.1 1.8e-08
x1:frailty(cluster) 0.00104 0.000746 0.000659 1.95 1.0 1.6e-01
x2:frailty(cluster) -0.00171 0.000642 0.000638 7.08 1.0 7.8e-03
Scale= 0.552
Iterations: 10 outer, 30 Newton-Raphson
Variance of random effect= 0.0522 I-likelihood = -5351.6
Degrees of freedom for terms= 0.6 0.9 1.0 71.1 0.8 1.0 1.0
Likelihood ratio test=224 on 74.3 df, p=<2e-16 n= 5000