When you've uploaded several CSVs and load the lists page to monitor import status, the lots of AJAX requests triggered by that list will end up slowing down the import itself.
Sendy seems to be asking for the progress of each pending list individually every 0.5 seconds or so, even though a single list gets processed at once (so most requests will return "0" as a result). After a couple of minutes, Chrome Inspector shows ~5000 ajax requests.
If Sendy only checked via AJAX a single list at a time we would reduce the requests significantly. Also, the interval between each check seems to be too frequent. It could wait much longer than 0.5 seconds (say, 5 seconds) and we'd be just fine. For 10 simultaneous CSV imports, that would axe the requests from 1200 requests every minute to just 12 requests.
(Sorry if I misdiagnosed the issue)