I've always sent my emails to
info@partypoker.com and that seemed to work fine for this problem and other questions I've had. I'm not sure if sending them a new email instead of replying to the same one will make a difference. I received a total of 3 emails from them and they were signed by 3 different people even though I had just been replying.
None of the emails I got (or their site) says that the bonus period started at 19:00 June 3. My withdraw was at 19:50. I think they have some confusion amongst themselves on this issue, or they decided to make it a solid rule after giving some people the bonus already.
I've never contacted Party support by phone, but it may be easier to sort it out with them that way. It would certainly be easier to talk to a manager or higher-up person that would be more likely to give the bonus. If the emails aren't working, I would try it.