Currencies don't always need a "symbol" for a particular denomination. Frequently a nickname is sufficient.
1 large (or grand, or G, or K, or stack)
There is a critical difference - everyone knows that 'dollar' is the standard unit, in the main, all software and formal presentation is in unit dollars, both because that is the standard unit, and because that is the normal scale for everyday transactions.
The logical comparison is much closer to 'cents' '¢' that to 'grand' (and while the US has quarters, dimes, and nickels, that is far from the norm)
The move to 'bits' is more fundamental, in that it will likely be the predominant usage down the line, and furthermore, will be the basic denomination coded into many systems, with satoshi 'cents'. For display purposes we, along with many other companies, will be showing values in 'bits'; and it is much better for the ecosystem to support quick understanding and ease of use of 'bits' in the everyday world.
You are trying to pin down a moving target and give a permanent symbol to a temporary slang name. It seems rather silly.
Sure, right now some people (including yourself) have decided that micro-bitcoins (aka "bits") "will be the basic denomination coded into many systems, with satoshi 'cents'", but this is only because that makes sense for the current scale. If a few years from now (or 5, or ten years from now), the value of bitcoins grows to the point where you can buy what today would be thought of as a $300,000 house for 3 "bits", then the scale will have moved and nobody will be see "bits" as "fundamental, in that it will likely be the predominant usage down the line". They'll simply move to a new slang name for a new scale.
It just doesn't make sense to potentially need to come up with a whole new symbol, and for everyone to have to adjust to the new symbol, everytime the value of bitcoin increases to the point where people become more comfortable talking in terms of a new magnitude.
Bitcoin was designed to eventually become deflationary. This means that on a long enought time scale as long as bitcoin exists, people will always be spending ever smaller amounts of bitcoin to acquire the same value of products or services. By its very nature the predominant usage over time will continuously change. Stick with nicknames and an extra character to indicate those ever smaller fractions of the base unit (the bitcoin), just like we do the opposite with inflationary currencies (using nicknames and an extra character to indicate the ever larger multiples of the base unit).