You can.
I did a remote proctored exam for the NREMT last year. They had me walk the camera around the room, under the desk, etc. All devices had to be in my backpack. No earbuds. They made me unplug the conference tv on the wall, lift picture frames etc. I had to keep my hands above the table the whole time, I couldn't look down if I was scratching an itch. They installed rootkit software and closed down all of the apps other than the browser running the test. They killed a daemon I run on my own pcs that is custom. They are recording from the webcam the whole time and have it angled so they can see. They record audio the whole time. I accidentally alt tabbed once and muted the mic with a wrong keyboard, those were first and second warning within 5 seconds.
When you take the test in a proctored testing center location they lock all of your stuff in a locker, check your hands, pockets, etc. They give you earplugs. You use their computer. They record you the whole time. They check your drivers license and take a fingerprint.
Those methods would stop a large % of your attack vectors.
As do the repercussions:
A candidate who violates National Registry policies, or the test center's regulations or rules, or engages in irregular behavior, misconduct and/or does not follow the test administrator's warning to discontinue inappropriate behavior may be dismissed from the test center. Exam fees for candidates dismissed from a test center will not be refunded. Additionally, your exam results may be withheld or canceled. The National Registry of EMTs may take other disciplinary action such as denial of National EMS Certification and/or disqualification from future National Registry exams.
At a minimum you're paying the $150 fee again, waiting another month to get scheduled and taking another 3 hours out of your day.