Adaptive Casting

It probably wouldn't break anything. It would solve your issue of General spells being a notational convenience, as Adaptive Casting existing essentially requires magi to recognize general spells. However, I think magi do recognize General spells. Let's say one magus casts Aegis of the Hearth (ReVi 20). Now let's say a second magus casts some spell that we note as Aegis of the Hearth (ReVi 25). What name do the characters use for the second magus's spell? If it's still known as Aegis of the Hearth, then the concept of a General spell is known in-character even if characters wouldn't use the term "General."

That said, while it wouldn't really break anything, it wouldn't fix much of anything, either.

Yes, this is one of the problems. As it exists, we can have situations like the following. Imagine a magus with Flawless Magic who has a General spell at level 30 with Spell Mastery 10. The magus spends a single season in the lab inventing the same spell at levels 5, 6, 7, 8, and 9, each time taking Adaptive Casting. Does the magus get to add +5 and remove 5 more botch dice when casting the level-30 spell?

There remain other problems that must still be addressed as well. This only addresses one of them.

Yes, that would be nice. There are some times the formula is tougher to write, like when the pattern goes 1, 3, 6, 9, 12, 15, ... That 1 there is tougher to include, but it would still be better to write it with such a pattern and a note about the exception with that first magnitude used.

There are also other guidelines that don't seem to have such a pattern due to wording, even though they do. Consider CrCo healing wounds: "Heal a Light Wound" v. "Heal a Medium Wound." The higher-level one does the same thing ("Heal a [severity] Wound"), it's just more powerful. Technically these qualify, but I don't think writing them as a pattern would simplify things for anyone.

That's a separate issue. I've always read the core rule "the maga may not exploit any other spellcasting options, as there is not enough time" (p.83) as saying you cannot do this.

Pretty much every magus I make. There tend to be a few spells that are so central to a magus's repertoire that it's worth sinking 5 or 15 experience from character creation or adventure into these at the very least.