TSFRESH - features extracted by a symmetric sliding window
If I understand your idea correctly, it is even possible to do this with only one-sided rolling. Let's try with one example:
You want to predict for the time 8:00 - and you need for this the data from 5:00 until 11:00.
 If you roll through the data with a size of 6h and positive rolling direction, you will end up with a dataset, which also includes exactly this part of the data (5:00 to 11:00). Normally, it would be used to train for the value at 11:00 (or 12:00) - but nothing prevents you to use it for predicting the value at 8:00.
Basically, it is just a matter of re-indexing.
(Same is actually true for negative rolling direction)
As raw data we have measurements m_{i,j}, measured every 30 seconds (i=0, 30, 60, 90,...720,..) for every subject j in the dataset.
I wish use TSFRESH (package) to extract time-series features, such that for a point of interest at time i, features are calculated based on symmetric rolling window. 
We wish to calculate the feature vector of time point i,j based on measurements of 3 hours of context before i and 3 hours after i. 
Thus, the 721-dim feature vector represents a point of interest surrounded by 6 hours “context”, i.e. 360  measurements before and 360 measurements after the point of interest.
For every point of interest, features should be extracted based on 721 measurements of m_{i,j}.
I've tried using rolling_direction param in roll_time_series(), but the only options are either roll backwards or forwards in “time” - I'm looking for a way to include both "past" and "future" data in features calculation.