I've had Speckled Sussex and many other similar sized chickens. They have no problems flying up and down from a 5' high roost. I've seen 2-week-old chicks fly up 2' and horizontal 3'. It was obvious watching them they could have gone a lot further if they wanted to. If your 20-week-old cockerel is healthy he should have no problems flying up or down if he wants to.
There are some conditions on that. With chickens there are always "if's". Show quality birds are usually pretty large for the breed. If they are really heavy they can injure themselves getting down. They may even have problems flying up. Is he that much larger than the rest of your birds?
If your coop is really crowded they may not have enough room to fly up and down. They need to be able to spread their wings and fly without bumping into things like nests, walls, feeders, or waterers. The higher the roosts the more clear space they need to land. If your other chickens are managing that, he should be able to also. As long as he is not injured I think it's a matter of "want to", not that he can't.
Do you have any adults in the flock, hens or roosters? Sometimes mature hens can be pretty brutal to an immature cockerel. Or a mature rooster may frighten him. Mine are most brutal to each other when settling down on the roost. My immature chickens very seldom use the main roost until they mature enough to force their way into the pecking order. That's such a consistent problem that I put up a "juvenile" roost. It's a little lower than the main roost, higher than the nests, and horizontally separated. That gives them a safe place to go that is not my nests. If your coop is big enough you might try something like that. You might need to set him on it a few times to get him to use it.
A week backpacking in Romania, that should be an adventure. Good luck!