If a `start_time` is specified with streaming, streaming doesn't work.

[sync-by-unito[bot]]

Expected behavior: stream all data captured after the start_time and into future. Actual behavior: data is streamed from the start_time to the present time, and then streaming ends.

┆Issue is synchronized with this Jira Bug by Unito ┆Attachments: b_http_data_stream.txt

[JamesMBartlett]

Going to handle this in #573