You are not riding in a 1/2 seat when out on the cc course. You should never be in a 1/2 seat out on the cc course.
What I see though, is that your seat is stiff - which is understandable because you're nervous your first time out - but the more you work on dressage as you said you are, you will learn to relax your pelvis and hips which allows your seat to remain in your saddle, and swoop with your horses canter motion.
Half seat is not the same as two point. Half seat is where your rock onto your crotch, lifting your seat bones off of the tack. You should never ride this way on the cc course.
Most people do a 1/2 seat incorreclty though. They think it is as stated above, but how it really should be is all 3 points remain in your saddle *two seat bones and crotch* and your upper body just moves forward slightly ahead of the verticle.
Your seat must always remain functional - on all 3 points.
Here are pictures to help you HoofPrints.
Top is 2 point. Middle is Full Seat. Bottom is 1/2 seat
When out on the CC course - you always approach every fence in a functional solid seat - now when you are hand galloping between fences, yes you merge into a 2 point to give your horses back a break - but about 5 strides to the fence, you sit deep, wrap those legs around your horses girth and support, encourage and aid your horse to that fence.
In your vids, you never once merge into a 1/2 seat. I would like to see you work on relaxing your seat though, keep it in your tack before and after the fence.
Good job though :) You're doing well.