Your calculation is similar to mine, with some alternations, like you used law of sines (I used law of cosines). But the main difference is, that you assumed constant deceleration. (By the way, in Butler case we calculated polinomials for a bunch of projectiles, see below.)
The problem is the degree of freedom (DoF). At almost any location choosen arbitrarily, you can find a bunch of pairs of initial speed and velocity drop. Actually infinite number of pairs, as a function. So what we could do is: calculate those functions (it is not a vector space nor a tensor space, but even worse. A space of functions. And we should compare all to each other. It is a sweating job, even for Laplace’s deamon.)
Butler:
unfold for details
By the way, once I used a special techic to slow down audio, more than possible. Each digital sample to be converted to one (or more) full period of sine. Here 2 second original audio takes 40 seconds.
https://drive.google.com/drive/folders/1Z1XggDLvgsMym_uFGEiJGGj68cZjTZf1?usp=sharing_eip&ts=691264ee