re: "When is an appropriate time to ask Upwork for help?"
You can't ask Upwork for help. This is between you and the client.
What is Upwork supposed to do?
If you can't do the job due to a technical issue on the client's website, then you can't do the job.
If this issue was really critical for the client, then the client would be in regular communication with you. The fact that you have not heard from the client tells you what you need to know about the urgency of the job.
One thing you should understand is that the due date you are seeing (April 20) means nothing to Upwork. Really. Upwork doesn't look at that or use it in any way. So don't worry about that.
You already sent a few messages. Send no more.
When and if the client bothers to read your messages, the client (who is a normal reasonable human being) will either get you the access you need on her website. Or she won't. I don't think she is going to be irrationally upset about something that was out of your control.
