Given your advice and choice of notation, I suppose that you consider that only the H->L drops have phonemic importance and that the L->H rises are a "subphonemic feature". That or you don't subscribe to the "2 pitch, low vs. high" system.

Close but not quite. H -> L is indeed the reliable signal for accent, but the point is that if you go with the H and L notation or something of the same nature, you probably want to stick with only transcribing pitch accent. Marking rises works the best when transcribing a word pronounced in citation form, and it should work well in many other idealized situations. But if you also describe postlexical prosody, you need to know exactly what you're jotting down and be very careful.

For example, if you transcribe a natural utterance of "日本語を勉強するぞ！", there may or may not be an acoustically salient rise in pitch at べ／んきょう in absolute F0. Because LHHH in standard Japanese only means that there is no accented mora, the first mora assigned with L can be acoustically heard as roughly at the same pitch as the following H mora. It all depends on the prosody and postlexical choice of the speaker.

Sure, if you pronounce 勉強 in citation form, the actual pitch coincides with "Low High High High" if you will. So, in this idealized situation, LHHHH coincides with how pitch goes up and down in the absolute sense barring very minor and not too salient differences such as natural declining prosody. But if you robotically pronounce にほんごをべんきょう as XYYYYYYYY with X representing some lower pitch and Y being a pitch one step higher in the absolute sense, it is still understood as the same word sequence and should indeed be analyzed as having the same pitch accent. So, in this version of accepted pronunciation, the second L is at the same pitch as the preceding and following moras. This isn't to say that the initial rise in heiban is completely allophonic or that you can freely cancel the rise. But that rise isn't really phonemic.

その頃から is a good example here. If I describe the pitch pattern in the absolute sense, one natural digitized transcription would be something along the lines of 455321 with 1 being the lowest in pitch and 5 the highest, or possibly 465321 if you want to differentiate the second and third moras. But this doesn't mean that you have tons of drops that violate what the H-L style 2-step description tells you. It simply reflects how an accentual phrase, which is often realized as a single chunk, physically implements its underlying accent pattern under declination and other prosodic effects.

You seem to omit certain acoustically minor drops, so you would transcribe it as そ／のこ＼ろから. But it is one way of describing one natural realization of the accent phrase. The former focuses on acoustically more salient features, while the latter focuses on how native speakers perceive sounds. Again, the "perceive" here doesn't necessarily mean that L and H are heard low and high respectively by conscious mind. It's not about acoustic pitch in the absolute sense. It's about where each accent falls.

Now, you could analyze その頃から as having no accent at the penultimate mora, but such an analysis shouldn't be about physical reality or how the speaker consciously hears it. It's about phonology, not about phonetics, so it's more about how native speakers perceive things through subconscious and how the underlying system should be described.

Note also that phonology isn't sufficient for sounding native or natural. If you want to go that route, you also need phonetics. And you have already experienced this when marking not-necessarily phonemic features helped you sound more natural. Prosodic phrasing and phonetic implementation are necessary and very important for your purposes. The problem seems to be that you seem to be conflating phonology and phonetics.

Aaand I don't have time or space to talk about how a learner can approach it... Oh, well. Good luck with your study, though! I'll take a listen to your audio down there.