Okay, so there is no real way to get PID values right on the money except with trial and error correct? And lower values are generally better then too high values so the vehicle over corrects.

Of course there are ways of setting PID gains "right on the money". It is called control system analysis and design. There are many books on the subject. You could even take some college courses. You can actually make a fine career of setting gains and wiggling fins. Even if you don't master the subject you could at least become acquainted with the nomenclature.

Continuous linear time invariant systems are the easiest, but you can use what you learn about them to help understand more complicated systems. Root locus is the classic tool to set gains, and you can do that with pencil and paper, although a Spirule can speed things up. In general, you can look at input/output response; Consider an input command or disturbance and see what the output result is. Inject a small or unit sinusoidal signal and sweep the frequency. Plot the output amplitude ratio and the phase shift. This is the frequency response or Bode Plot and it can give you the gain and phase margin, or where you have stability problems. Consider the response to a step input: What is your rise time, peak overshoot, and steady state error? Or consider an optimal control approach, the Linear Quadratic Regulator, LQR. You could for example pick some weighting factors to try and minimize induced drag and battery power consumption. You will have to solve an Algebraic Matrix Riccati Equation, but that is a solved problem, and it will determine the optimal gains that you seek.

PID control is often ideal for a regulator. That is, to hold a system at some desired condition in the face of disturbances. Consider the step input response: to decrease the rise time increase the Proportional gain (and or increase the control fin size). If the peak overshoot is too high, increase the Derivative gain. Add some Integral gain to control steady state error. Repeat the adjustment or tuning until you get a response "right on the money."

Now a rocket is not a linear time invariant system. You could do a number of LTI point designs to find suitable gains over the range of flight conditions and smoothly change the gains over the flight as q, mass, CG, and inertia change. Most likely you have purchased some black box components that you do not have complete specifications and analytical models for. They are likely sample data subsystems and they may not even use the same sample rate or synchronicity. Your actuators will undoubtedly have rate, power, and position limits, as well as gear backlash, stiffness, linkage slop, etc. You could have a limit cycle oscillation, overheating problems, and a thousand other problems. You probably don't have the time and expertise to work through problems. On the other hand, plug and pray may work.

A rocket is also not a typical drone. Rockets bodies are flexible with mode shapes and frequencies. You want to put accelerometers at the first bending node, and gyros at the antinode. You will want an analog bandpass filter to attenuate sensor response beyond the sampling frequency, and you may need notch filters at the mode frequencies as well. Isolating the sensors with foam can also help.

It's almost like this is rocket science or something. In any event, dogs are better than cats.