I'll start with different people are different, and what works to communicate with one person may not work for others. It's possible you'll need different techniques for one or more of your friends.
I also tend to be a direct person. But it's also not always about how direct one is; for some people it's about the apparent potential for confrontation. Your example where they disappear rather than responding to a question of their availability sounds more to me like that than about how direct you were.
That said, you know your friends infinitely better than I do, so I'll assume you're right. The most common way of indirectly inviting your friends to hang out on Thursday night is to just casually mention that you were hoping to hang out with your friends on Thursday night. For me, and probably you as well, this sounds like an assertion that you're going to be busy, but I know people who need to be invited with that language. I am somewhat averse to using it, because not only does it not sound like an invitation to me, but I've had times where I tried to use it and the person I was trying to invite felt excluded, despite the fact that they were also averse to my more direct invitations.
Alternatively, back on my initial reaction, it could just be how you phrase it.
Are you free this Thursday night to hang out?
can sound like a demand to some, and they really don't want to say no, but they are also opposed to saying yes. I've had friends who later on admitted that they actually had been free, but really didn't want to set a precedent of doing whatever I said. That sounded completely crazy to me, because it wasn't my intent at all - but they'd known some people who were very controlling and happened to use that same language sometimes, and so it triggered that reaction. If that's the case, avoiding all ways of phrasing things that some other person you've never met has used could be very difficult.
Sometimes you just have to try some variations and see what works. I've found things that were more direct about accepting a no answer have worked more frequently with those I've talked with. Some of the variations I'll offer here would also fit in with the indirect wording to an extent, but in these, I'll always be explicit that they are intended to be included.
I'd like to hang out with you this Thursday. It's fine if you're busy or just don't want to.
I'm hoping to hang out with some friends on Thursday. Would you be open to that? It's OK if you're not interested.
I'm really busy most of this next week, but I'd like to spend more time with you. I'm not doing anything on Thursday. Would that work for you? It's fine if you can't, it's just the only time I have this week.
Some people might want more of an idea of the activities that would be done, while others prefer having things left open. Some people might want a choice of days or times. That might be an option, given your schedule, or it might not.
Edit: I have also known people who didn't like being pinned to a specific time to hang out with a particular friend when they believed that their friend had no reason for wanting to narrow things down to a specific day or time.
I've most witnessed this friction around trying to get commitment to show up to a surprise birthday party or something like that, but I also knew someone in school who always tried to get friends to hang out with him on one specific day of the week each week - although which day would change week to week. This person's friends saw them as a child of wealth who had nothing to do with his time but wanted to get his friends to bow to his arbitrary schedule because he was controlling.
I later found out that he was not as wealthy as his friends thought. He always seemed to have money to spare, whether it was for the latest gadget or someone in need, so they figured his parents were so loaded they didn't teach their son economic sense. But actually, his family was slightly less wealthy than theirs. He just worked at the family store 6 days a week, with barely enough time to do his homework on those days. He just had his own money because he worked his butt off to earn it.
Letting his friends know why he didn't have time made it much easier for him to schedule things with his friends on his weeknights off. But in his case, not doing that wasn't a lack of interpersonal skills, it was tactical. He waited to do it until he found a different group of friends who would both not disrespect him for being a working man and not try to hang around his store while he was working trying to distract him in the name of friendliness.
Explaining why you want to schedule for a certain time can be helpful, but it's important to consider the consequences of giving out that information. Most of the time, for most people I know, it's better to give out that information to maximize the chance of having the person be more agreeable to the restricted schedule.
There are some people who would prefer to not know why. Different people are different, and they have their reasons. There are also times like my classmate had when it's better for you to not share. I don't really have a good heuristic I can relate as to when is a good time to share and when isn't, but I think that would count as a separate topic anyway.
