epochs realignment: shifting time by variable length on each epoch.

Describe the problem

I have a dataset where subjects listen to a series of 4-5 tones on each trial. However, the Inter Onset Interval between tones is different from trial to trial. I would like to create a function that allows me to realign epochs so that the 0 in epoch.times is now centered on the 2nd, third, final, etc tone. Typically this is done by altering the event array directly. However, because of the series of tones, I still want my baseline to always be before the first tone where there is silence.
So I want to be able to:

1. define large epochs that cover all tones in each trial
2. Apply a baseline, timelocked to pre first tone, in an epoch by epoch manner
3. Realign epochs to a specific tone in the trial. Critically, this shift would be by a different amount for each epoch so epochs.shift_time wouldn't work.

Describe your solution

I have found a solution to do this outside of mne and would like to implement it in a TimeMixin so that it can be used for both Epochs, EpochsTFR and wherever else there are multiple trials with time stored, (Source Estimates?).

It's a bit ugly and hard to follow, which is exactly why I think we should implement it so that it's well tested and users can avoid the potential errors when they try to do it outside of mne. Here is a very basic example which shows the concept of the method.

import numpy as np
t = np.round(np.linspace(-.5, 1., 16), 1)
sfreq = 1. / (t[1] - t[0])
n_epochs = 3
# faux data, 3 epochs x 16 timepoints
data = t * np.ones(n_epochs)[:, None]

# How many samples to shift for each epoch in realignment
sampshift = np.array([2, 4, 6])

# realigned epochs must have smaller window than original epoch
new_tmin, new_tmax = -.2, .3

# indices to extract the correct realigned samples
minsamp = np.round((new_tmin - t[0]) * sfreq).astype(int)
maxsamp = np.round((new_tmax - new_tmin) * sfreq).astype(int) + minsamp
idx = sampshift[:, None] + np.arange(minsamp, maxsamp + 1)

# needs some checks here to make sure you don't exceed epoch size
shift_data = data[np.arange(n_epochs)[:, None], idx]

I would also like to move some methods like .shift_time, maybe .crop into the TimeMixin so that they are not implemented in multiple places. This could be a separate PR.

Describe possible alternatives

Another alternative for my specific problem is to allow for different baseline windows for each epoch but this doesn't seem to me to be a good practice generally and I'm not sure how much we want to encourage people to draw baselines from different timepoints in a typical use case.

Start by reviewing the TimeMixin proposal and the existing shift_time and crop behavior on Epochs and EpochsTFR. Use the example's per-epoch sample shifts and baseline requirements to define the API, then determine how Source Estimates or other time-indexed objects fit. Done means variable shifts are safely applied per epoch with bounds checks and tests cover the realignment behavior.