This is my suggestion and it worked fine on my humble laptop. You could supplement it with means test to make sure the sample is sufficiently reflective of the population.
data1 <- read.csv("stackexample.csv") ##read in dummy data
library(dplyr)
library(sm)
data2 <- sample_n(data1, 10000) # make statistics work for you -- sample the data
sm.ancova(x = data2$s,
y = data2$dt,
group = data2$dip,
model = "none") #non-parametric ANCOVA

Even with a sample of only 1,000 I didn't find any significant differences in the means.
t.test(data1$s, data2$s)
Welch Two Sample t-test
data: data1$s and data2$s
t = -1.4469, df = 1017.9, p-value = 0.1482
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-37.657822 5.692622
sample estimates:
mean of x mean of y
125.3137 141.2963
With a sample of 5,000:
data2 <- sample_n(data1, 5000) # make statistics work for you -- sample the data
t.test(data1$s, data2$s)
Welch Two Sample t-test
data: data1$s and data2$s
t = -1.0653, df = 5513.7, p-value = 0.2868
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-14.736700 4.359704
sample estimates:
mean of x mean of y
125.3137 130.5022
t.test(data1$dt, data2$dt)
Welch Two Sample t-test
data: data1$dt and data2$dt
t = -0.069479, df = 5507.8, p-value = 0.9446
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-18.39645 17.13709
sample estimates:
mean of x mean of y
515.6206 516.2503
t.test(data1$dip, data2$dip)
Welch Two Sample t-test
data: data1$dip and data2$dip
t = 1.2044, df = 5536.3, p-value = 0.2285
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.6268062 2.6241395
sample estimates:
mean of x mean of y
126.6667 125.6680
and of course, you can use more/difference statistics to validate your sample depending on how far you want to take it. You could also estimate a Power Curve beforehand to determine the sample size.
With a sample of 10,000 it took about 3 minutes to complete on my laptop. With a sample of 1,000 it finished instantly.