I can see that it is difficult! It seems that you have one particular school in mind - unless it is very popular things do often change, and even if they say you need to sign up now to secure a place, there might well be places even later on, if you want to give it some time. Attending year 10 sounds like a given for him in any case. It is 18 months away, do you think it might be good for him to get away from home, if many of his friends might be going to gymnasium?
One of my Danish friends actually lives in Sweden, and her child didn't speak Danish. They have heard it a lot of course but didn't speak it. They love it now, perhaps especially the fact that the grades don't matter that much! Wouldn't it be the same case for your DS since he could still apply with his year 9 grades if he wanted to?
Remember that the efterskole has seen it all before :-) They are very used to dealing with children who are homesick, they do a ton of 'getting to know each other' exercises etc to make sure people get along/get friends etc. If you decide to send him, I think the important thing is that you go for it fully - don't 'bribe' him with things like 'you can leave at the efterårsferie if you don't like it' etc - he needs to try, and if there are issues, speak to the school, trust them to provide support so that you work with the school, not 'against' them if that makes sense.
Also re homework - I think there's quite a strong focus of doing your homework, often 'quiet time' every day when they're not allowed to use any electronics and have to be in their rooms, so not much else to do, so to speak.
Have you lived in DK long or not so long? Might it be a strange concept to him that might make him hesitate (English people I speak to here often find it very odd, there's such a focus here on going quickly through school and university, and taking your time to choose and figuring out what you want to do in life just isn't standard/appreciated. Also remember his Danish will be sooo much better then, I'd say it's unlikely he'll need language support if he already kind of gets by.
I think you'll find that there are very few children whose years are total disasters! But of course there is no guarantee. Why don't you check with the school if they could see if a current parent would be willing to speak to you about their experience, perhaps a parent of a child who is not super socially confident etc?