Your questions tell me that you need some basic explanations of how this all works.
I'm going to ignore vacuum advance because you seem to be concerned with performance, and under "performance" (wide open throttle) operations the vacuum advance mechanism is inoperative and is doing nothing.
Inside your distributor there is a system of weights and springs. As rpm increases, the weights pull against the spring tension and rotate the spark triggering mechanism inside the distributor to occur earlier and earlier. There are mechanical limits to this process - a starting point for the weights (engine off) and an ending point (weights have moved as far as they can). This total range of weight movement is what determines how much advance (called mechanical advance or centrifugal advance) your distributor is capable of providing. In your case, your distributor is capable of providing 19 degrees of advance. Coupled with 15 degrees initial, that's how you get to 34 degrees total" 15+19=34.
If you want more total (38) without having to add more initial, then you will have to modify your distributor internally so that it has more range of movement for the weights.
Now some answers to questions you didn't ask.
Why do you think you want 38 degrees total? If your engine is a real RA III and has RA III heads, 38 degrees total is very likely to give you LESS performance than what you have now, not more. RA III heads are open chamber design and as such have very nice flame propagation characteristics and good combustion efficiency. They don't require as much "lead time" (advance) to develop maximum effective cylinder pressure (torque) as other heads (for example the 1967 '670' heads) do. By lighting the fire earlier than necessary, you're building cylinder pressure while the piston is still on it's way UP in the bore and you're essentially trying to make the engine run the other direction. This is not how you make power
If you want to dial your car in for max performance by playing with ignition timing, there are only two ways to do it. 1) On a dyno 2) at the drag strip with a set of accurate timing clocks. Start with a setting that you know is lower than what you need (in your case, I'd start around 32 degrees total). And then start dialing in more advance 1 or 2 degrees at a time, taking fresh measurements after each change (another dyno pull or several quarter-mile passes) until you find the point that makes the best power / produces the quickest times. Generally this means finding the peak and going past it some (where performance starts to fall off again). That peak point will be the best setting for YOUR engine.
Why are you concerned about running 15 degrees initial? As long as the car starts easily and doesn't overheat, the initial timing setting is of very little consequence. What matters is the total.
Ignition advance is NOT a case of "more is better". Best results come when the setting is optimized for the combustion characteristics of your particular engine. Lighting the fire too early is just as bad (if not worse) than lighting it too late.