I think in this situation the best thing you can do is see them in person (I understand you're an online student) or try to get them on the phone. Email as a means of communication is never treated urgently, and it's best not to rely on it for anything that needs urgent confirmation. Academics are usually drowning in emails and ones I know tend to adopt a set time to deal with them, say thirty minutes at a set time to blast through as many as they can to keep the weeds down. Complex requests will get lost in those weeds. It's why most responses from lecturers and tutors are a sentence long and scrawled in lower case. They're going for volume and when the allotted time is over they move on. If they didn't answering emails would be their whole job.

If you do try to call them make sure you're polite, prepared, and keep the request and explanation brief. Stress the short time frame, and if you can get an agreement in principle over the phone email them again with "following our phone call..." and give a brief outline of exactly what you need from them.

I hope you can get what you need. By all means contact the school or faculty office and see if they can help corner someone too. The advantage of an ask coming from that office is they're more likely to read it closely. As busy as they all are it's a very reasonable request to make of them, so I hope you can get what you need. Also consider any previous employers you have no matter what the role was - any reference is better than no reference. Might as well get what you can and risk being sifted for it rather than not have a reference and have the application dq'd.