Mathematical model of equivalent-time sampling, the resulting unevenly spaced periodic signal, and its interpretation
Since the physical measurement takes a certain time $t_s$ (leading to the original sampling rate), each sample in $s[t]$ can be seen as a convolution of a sampling function (perhaps a boxcar) $f(T)$ with the continuous physical value function $s(T)$ during the measuring time. I suspect this is different in the questions that are linked above, which regard economical data and might be regarded instantaneous values.

If that is correct, then in equivalent time the highest frequency that is sampled should not be higher than in the real / original time. Unless there is some way to deconvolve the measurements in equivalent time, the sampling rate in both timeframes should be equal. So the high number of samples between the start and the end of the average period should be reduced to match the true sampling rate, before comparing two measurements.

I think that a moving average with subsampling can be performed. This should be set such that the resulting sampling rate equals the original one. Since in equivalent time the samples are unevenly spaced this can not be performed by a filter in the frequency domain. The moving average has to be performed in the temporal domain instead.

Scale phase $\varphi$  to the average period $P$ of all $N$ periods so its unit is equivalent to that of $t$

$t'(\varphi) = \frac{\varphi}{N} \sum_{i=1}^{N} t_{i,end} - t_{i,start}$ to give $s[t']$

Moving average of $s[t']$ for every $nt_s$

$s'[nt_s] = \frac{\sum_{t'\geq (n-1)t_s}^{t'\lt nt_s} s[t']}{\sum_{t'\geq (n-1)t_s}^{t'\lt n t_s} \frac{t'}{t'}}$

Im not sure about the notation since every $t_s$ has a different number of samples and the period length is not equal to an integer number $n$ of $t_s$. In practice you could append $s[t'+P] = s[t']$ and then use $t_s' = \frac{P}{ceil(\frac{P}{t_s})}$, leading to a slightly interpolated result, but at least it is truly periodic.

The resulting waveform has no more detail / higher frequency content than the original signal. This signal can be compared between experiments like any other signal, so at least it is a workable solution. 

This might be a poorly constructed method compared to other suggested solutions (Kalman filter, non uniform FFT´s gridding and unevenly spaced time series operators), but its probably easier too. Not sure if I lose any information in the process.