Insufficient AC to bedroom from unit in rear

If you want to spend a bit more, you could put in a vent fan (Fantastic, Maxxfan, etc). You could then set it to blow air out, and it will suck some cooler air into the bedroom. At night, reverse the flow and blow cool air from outside in.

That is what we do.

I had the same problem. After reading several postings on this website I took the vent cover off the inside of the unit. I found that one of the outlets was blocked about 1/3 shut with expanding foam. That was removed with a sharp knife. It helped some with the airflow. We then bought a small fan and place it just before the bedroom door facing towards the bedroom. That helped. Not perfect but its better than installing a 2nd air conditioner.

In 2010 we bought a Cameo in Colorado. We thought we might be fine in Texas, but found out even with the ducted air going into bedroom it was not adequate. When its hot even in a trailer with good insulation it just won't cool the entire trailer. Trailer was prewired so had a 13.5 unit which make all the difference. Will make sure we always have 2 units for now on.

If the A/C is in the very back I don't see an other way other than getting a second A/C, Even with all other vents closed, air will still leak out and it will warm up as it passes through the ducting. You could get a 9k BTU and use that just for the Bed Room. I had a similar problem with my 5th wheel. Even though It had 2 A/C's they where both in the front most half of the RV and too cool the bunk house I had to run both A/C to get the air to push out COLD out of the 2 bunk house ducts. But then I noticed the pre-wiring for a 3rd and got a 13.5k BTU Power Saver model which only pulls 11 amps vs. atleast 15 amps for normal 13.5k and 15k. And I plugged up the ducts so each A/C has Its own zone. So now the cooling is more effective and controlled.

You could set up a fan to blow the air from the living room to the bedroom when needed. Would be difficult to add another duct to the bedroom.
Surprised you only have one bedroom duct. Our 5er is shorter than yours but has two bedroom air ducts and puts quite a bit of air there.
We did add a 2nd AC, but in TX and the southwest it is needed and we usually have 50 amp hookups.