What has worked well for my beardie (got him as a baby) was sitting in the same room, next to the enclosure, and just being there, doing quiet things. Things like reading, working on a laptop...
After a while, he started watching me instead of hiding.
After a longer while, each time when I opened the enclosure, I touched him briefly (for a second or so) in case he was within easy reach (never catching him, never doing things like lifting a hide he might be under). Continued this with hand feeding, then after a much longer while with just picking him up inside the enclosure (also only if within easy reach) and setting him down again after a few minutes.
Each step only if he completely tolerates the previous one.
Get him out near bed time and let him fall asleep while setting on you.
Could be an option, depending on his routine. I would just not catch him.
(I have never taken him out near bedtime as he goes down in his burrow anytime between 6pm (then stays awake for some hours, just resting) and 9 pm (then sleeps soon). Him sitting on his branch, watching us while we have dinner, then he either might be down in his burrow "in a second" or he continues basking.
But beardies are so individual and for some this might work. I guess one can even get them used to this routine if it works initially, like for your dragons.)