I think the best approach would be to perform your deployments from Jenkins. This would have a number of benefits:
- You're not stuck with the cluncky UI the cloud portal uses and could implement funtionality to actually deploy with a single button press.
- You're allowed for greater flexibility as to what environment to deploy to. It would make sense to have an extra environment that you run all your selenium tests on, since it would allow your test sutie on lots of new revisions without interfering with manual testing on your test environment. You could even consider doing this on an on-premise server without a license, as long as all your tests take less than 90 minutes to complete.