I'm going to flame you a bit, and say; if you want to have a happy healthy monitor, you're going to have to learn to think, and not just follow instructions you read somewhere. Because lots of crap is written about monitors.
Now just think for a minute WHY people would recommend separate feeding cages. The theory goes, if you feed in the cage, the (snake) will learn to expect food whenever the door is opened. By feeding somewhere else, you prevent the (snake) from associating someone at the door with a feeding response (bite).
But hey, you are talking about a MONITOR. A monitor is a thinking animal, not a simpleminded snake. They know perfectly well, if you have food or not, regardless of where they are. They also know the difference between you and food, in my experience. And they truly don't want anything to do with you. They're not that stupid.
Now how would your monitor feel? Being picked up (stress), taken out of its home (stress), and offered food. The monitor may very well decide food is the last thing it wants at that moment. Every monitor handles stress differently, but you said you are getting a BRN, and they are shy and sensitive IMO. Do you think it would even want to eat, when something bad is happening to it? (You took it out of its cage)
Please try to lessen stress for your monitor. Speaking about the shy BRNs, a BRN may not even eat in front of you, though they are hungry. They may not bask, even though they need the heat. Think of ways you can let it hide and feel secure. These guys need it.
And please don't just blindly accept crap you read, this post even. When you read something about them, THINK, from the monitor's point of view. Your monitor is depending on you. Good luck.
D.