I know that it's possible to selectively ingest in the import dialogue, but is it possible to delete "rejected" portions of clips once they've been imported, without deleting the whole clip? If not, what are viable workarounds?
It depends on your method of encoding, but with many formats, you can not simply cut a clip at a point of your choice without running in to other issues related to how the file is stored. It might be possible to do it within a few seconds of the desired point, but it's not frequently done in an editing application itself since that isn't the point of an editing application.
What you want to look for is an application that is capable of splitting the file format you are working with. Quicktime itself can do this for at least some MOV formats. Once you have split the file in two, you can delete the unnecessary portion and import the part you want to use.