When asking hard questions like this, it tends to be better to explore variations yourself with the help of AI, rather than throwing a million playouts at the starting position. It’s also far more interesting an exercise 
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Seeing as the OP has stated that they are not interested in the wall games, I’ll just make one more post about it here, and if anyone other than me is interested we could maybe start a new thread
Long post
To recap the findings so far, it seems like in an 8x8 area an invasion should die, while in an 9x9 area it should be able to live (this is by no means certain, just my current guess based on KataGo’s variations). So the most uncertain question so far is whether it’s possible to live in an 8x9 area:
In this position, black is winning by 15.5 points (area scoring, 7.5 komi). The smallest living shape has an area of 8 (causing a point swing of 16), so if white can live inside, white will win. (the smallest seki I can come up with also wins by 0.5 points)
I added the eyes in the upper left corner just to ensure that the black group never has to worry about its own eyes, regardless of how crazy the variations get.
Just looking at the initial position, KataGo gives close to 50% winning probability to the 3-3 invasion:
In other words, it can’t tell yet if it should live or die. So let’s look at some of the continuations!
I find this move 9 quite beautiful, a really loose net, which black can’t escape without giving extra forcing moves to white.
Here’s one continuation from the above where I didn’t let KataGo think very long on each position:
Isn’t that a lovely killing move at H4?
Turning to a completely different variation, this 3 looks promising for white:
Next B2 or B3 are the main options for black. B2 gives white a lot of forcing moves…
But after all that it’s still 50-50 whether white will live!
Here’s a different option, taking it more slow and steady with B3, but then going very aggressively for the eyes with 7 and 9:
White tries to exploit black’s weaknesses, but after 6 there is only one gote eye along the side, and KataGo gives black 93%.
This variation is a clear example of how much the distance to the wall matters. If black tries the same thing in the 9x9-area, there is no potential connection at G1. This means that white already has an eye along the side, and only needs to worry about finding one more in the center area. KataGo heavily favours white in this case:
I’ll leave it there for now. As you can see, 8x9 is very complicated! Putting some trust in KataGo’s winrates and variations, I’m somewhat confident (80% or so?) about 8x8 being secure and 9x9 being invadable. But for 8x9 I still have no idea one way or the other.
Apart from getting a strong player (or just someone with a faster computer than me) to analyze this position, one fun idea would be for two humans to play many times from the same 8x9-starting position. I would probably be more confident about killling than living myself, but that might vary from person to person!
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All these setups could inspire a new class of “shape game”-like variant. Even if a superhuman bot might settle the question for a particular corner size, it could still be an interesting game for mere mortals.
Choosing the size of the corner gives a natural way to handicap this game for differing skill levels.
Anyone want to play a game of this “big corner invasion” variant?
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Of course I want to play it! 
I sent you a challenge for the 9x9-invasion.
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The game is underway, in case anyone wants to spectate/kibitz
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Round 2:
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Interestingly, the human data, so far, suggests that invading 9x9 dies, while invading 8x8 lives!
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You might also be interested in my recent thread about the 3-3 invasion beneath the “cloud shimari” or 5-4 + 5-3 enclosure.
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In your very first diagram (with 3 stones) black is comfortable. he can easily run out or make eyes in the corner. A play at 4-4 gets out. Also black can attach underneath or play kosumi twice.
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Going a little bit deeper on Sensei lib
https://senseis.xmp.net/?10x10CornerGame1
I used many times this kind of position to show beginners how big a territory can be (and how 2 eyes don’t have to lie already on the board)
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Not only does it matter whether there are opponent stones nearby, it also matters how strong those nearby opponent stones are. For example, if white has the corner entire surrounded by a living group, even a bit further away than your examples, then an invading black at 3-3 is dead, because its eyespace can be reduced so easily using white double-skip or large-knight’s links from the white group. (My comments might be redundant to the comments about walls; they are just meant as a reply to the OP.)
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I gave this one a try and found that I had to expand the playing field to a 12x12 corner for there to be any significant chance of life, but KataGo thinks White is likely to win:
I think this is about as big as I can go without messing with komi. No idea if it means anything.
It seems like AI is happy to solve “black to live” or “white to kill” tsumego in this configuration. For example, here’s what it thinks of Cho Chikun Intermediate #41:
spoiler alert
(Is that a hard one? It’s available as #42 here.)
And here Black only needs the tiniest territory to win. I don’t think this would be a good way to evaluate whether a particular opening slightly favors white or black.
If black can survive at all under the aggressive attacks, it seems like that means he’s probably going to live on an empty board and in many other situations. I would like to have a collection of such strong positions involving the 3-3 point to study for use in games!
Some real game relevance (from this 11x11 game!):
I don’t remember exactly what I was thinking, but I suppose that somehow I considered my two 3-3 stones to be strong, A to be a safe way to claim another corner, and B to be a hopeless invasion. So I played at A and gave up on B.
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A safe way? I dunno it will give a chance to play a double attack move on the Left by black
Exactly what happened! I had to think hard before saving the top group, and then the bottom one became a really tough fight. Somehow it worked out well.
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