I can think of three ways. First one is for if you're feeling lucky; the second one will require manual sifting, and the third is a different approach.
Increasing speed in editor usually means undersampling the footage i.e. showing every nth frame. So, try trimming the in-point of the original unspeeded footage by a few frames, say, half a second's worth and then apply the speed change. That should offset the undersampling selection by those many frames. You may get lucky and retain fewer 'blinking' frames in the final result.
Increase the speed of the original footage to create a result of around 2 minutes. Let's say your final output is supposed to be 20 seconds. You now have to trim 5 out of 6 frames. So, scan the result, split the footage every 6 frames and keep 1 in each segment, deleting the rest. This will be time-consuming, but should work as last resort.
This might not create a smooth timelapse but could be acceptable. Select 20 one-second segments at around equal intervals from the original unspeeded footage. Join them together and extend the clips at the joins by 4 or 5 frames (on both sides) to create a 8-10 frame dissolve. Since the segments are curated, you can avoid all blinking. The chief issue here would be subjects' motion across segments. You'll have smooth motion within a segment but could have a 'jerky' change during a dissolve. So potential for a weird visual rhythm.