Old wood windows
My recommendation for your window would be our Series 500 spiral balance, along with our 17-012 bottom bracket (sold separately). We've been using these two parts to repair old windows like yours for decades and I'm very confident that they'll work for you. Look them over and let me know what you think!
So for a bottom sash that is 27 inches high (24 inch glass height), what size (length) Series 500 spiral balance should I get? (Seems like a 27 inch spiral balance would not have any room for spring to release/retract?)
So, the rule of thumb for wood windows is to add 3" to the visible glass height on the bottom sash, and 1" to the visible glass height for the top sash (if relevant). So if your bottom sash has a visible glass height of 24" then 27" would be my recommendation after all.
If you think that would be too long, then you could opt for a shorter balance and see how that works. In a worst case scenario you could drill a new installation hole for it a little lower to compensate and make up the difference. The catch to that is that the window would then not be able to open as wide.