Hey there. That was a really thorough explanation of the difficulties you're having, though some might see it as a lengthy essay. lol For starters, welcome to fighting games!
You sound a lot like me when I first started playing fighters. I say that because I also considered myself an offensive fighter, and having trouble in the corner in every aspect you described happened often against the better players.
I can't say for sure without watching you play, but beginner players often fall to anticipatory moves because they use the quickest move possible, which believe it or not isn't always the "best" way out. Even if you anticipate your opponent's blockstring gaps, keep in mind that they know their gaps better than you do, this Sol player may even be ending his blockstring early to purposely bait a jab or to quickly go to another blockstring.
You may find that countering with less regard for how long you must block may help you. Guessing is a part of fighting games too. When you start asking "what move do I use?", it may be a sign that you're thinking too much. Your opponent also has to guess from time to time.
Since you say you've been spectating fighters for a while, you may have heard terms such as "Plus on block" or "minus on block". These refer to the number of frames your opponent (or you) are "stunned" after having an attacked block (or blocking an attack). Some fighters will end their blockstring early to start their next string of attacks quicker. The gap may not be where you think it is, and you will have to experiment to find the timing.
In reality, you often only have a chance of getting out of the corner once pressured in. There is no guaranteed way out sometimes, because they are covering as many bases as they can and accounting for the ways you can guess out of the corner, compared to your character who only has a few moves they can pull off from blocking. Certain characters are also much weaker in the corner than others to compensate for their expertise outside of it (keepaway characters often fall into this category). I would check with the sub-forum for Millia and get their experienced advice on the matter, but it would do you some good to show them your gameplay.