Render and replace several clips as one

Hi, community. I have a problem. There's a voiceover and a separately recorded screencast, they are not similar since the client recorded them on different days, and now I have to adjust the video to what he spoke about in the voiceover. The problem is that the parts recorded and spoken have different length, so normally I would take a part of the voiceover and make the screencast-part the same length. But since during the screencast the client made mistakes and redid several actions again and again, I have to cut those parts, and finally we come to the problem - once cut, the prepared part is still longer than the voiceover so I have to speed up the video to shorten their length. I cannot speed up all the cut clips at once with the rate stretch tool as it stretches only separate clips. I cannot use nesting as somehow the nested sequence once sped up reveals the parts of the clips I've cut off (let us say I cut the clip right after my client has changed the color of the pen he's using to write a word but once the clip is put into a nest and the nest is sped up the part with changing the color reveals as well - this may be a bug, idunno). So the most convenient way for me to do this part would be changing this set of cut clips as one whole clip, merge them somehow, but Premiere pro can only render and replace separate clips and renderin - rendering a nest is not available - and rendering them out everytime is not a fast and convenient way to work. Any suggestions?