... What would you recommend me to do?
Video safe areas should be respected. They exist for a very good reason.
TVs & monitors, even many modern ones, underscan & overscan in varying amounts, have various kinds of plastic/metal frames around their screens, or are out of adjustment. It's quite random. This is why safe areas exist.
In future shoots you should reference a pro monitor which has a proper underscan feature enabled to determine correct/safe framing. Some cameras can display safe area frame lines superimposed on your "monitor" (not recorded) video. There are also frameline generators available you can connect between your camera and monitor.
In cases where this isn't possible, you need to leave ample room (>10%) all around the edge of the screen and your subject while shooting to more than accomodate TV safe area. Obviously this may result in less than ideal framing, but the alternative (undesireable elements within frame) is worse.
For material you've already shot, you can usually blowup/magnify video 5-10% or so in post to push undesireable elements off-screen without overly degrading the image, but results will vary depending on the quality of the original recording & format and the capabilities of your post environment. This approach is the least desireable because it may result in your subject being cropped and the image being degraded.
Clearly the best approach is to frame your footage correctly to begin with, allowing for TV safe areas. There are alternatives, but they typically involve compromises.
Just my $0.02 US.
All the best,
- Peter DeCrescenzo