So its okay to break the rules when it suits you, or convention?
So, show me that 0.999... exists in reality, and I'll concede 1.999...9923 is invalid due to it not being valid for giving directions across a pond.
It's not breaking the rules. When you prove stuff about ramanujan summation you never say it is also true for normal summation, unless you have a proof that it is the case. And a correct mathematician will not go around claiming that ramanujan summation is the same thing as summation, unlike Numberphile did...
You are right that existing in reality has nothing to do with maths. The problem here is getting different mathematical objects confused because they have similar names/notations.
As I said earlier, meaning an infinite number of digits by... either means you are no longer using real numbers, or it's a redundant notation as it adds no information.
0.0000...01 is 10^(-infinity), which depending on what you mean by to the power of -infinity, is either zero (if it is shorthand for a limit) or an infinitesimal(if infinity is a member of your new number system). If it's zero, then the part "after infinity" is redundant, it's just adding 0. If it's an infinitesimal, then you aren't representing a real number.
So 1.999...9923 is either not a real number, or is the same as 1.999... . Either way, is means 1.999...9923 is not a real number between 2 and 1.999..., because it's either equal to 1.999..., or it's not a real number.
Whenever I say real number, I mean a member of the unique complete totally ordered field (up to isomorphism), not that it is a reality number. Thanks of the confusing name René.