With no offence being intended or any desire to start an argument, I have to say that this feels like your inference based on what was said in the DoBJG entry. I don’t want to trouble you with running around looking things up and quoting relevant passages (because it’s time-consuming), and your idea of ‘emphasis […] on the second half’ does seem plausible, but I personally think that ‘emphasis’ may not be what changes here. For that matter, given this:
I dare say that emphasis might even end up on the first half, because んだから includes an explanatory のだ, which also tends to add emphasis. (It’s like そうですか vs そうなんですか.)
I decided to open up the 大辞林 dictionary and have a look since I found this matter very intriguing. Here’s what’s said under the entry for ので:
〔理由・原因を表す接続助詞「から」との相違について。「ので」は因果関係が客観的事実に基づいているような場合に用いられるのに対し，「から」は，推量・禁止・命令・質問など，話し手の主観に基づくような場合に用いられる。一般に，「ので」は，「から」に比べて，条件としての独立性が弱い場合に用いられる〕
My translation (N.B. I’m not certain about how to interpret the last sentence, even if it seems translatable):
‘About the differences compared to the conjunction から, which expresses reasons and causes. As opposed to how ので is used in contexts where cause-and-effect relationships are based on objective reality, から is used in contexts where they are based on the speaker’s subjective perspective, such as for suppositions, prohibitions, orders and questions. Generally, ので, as compared to から, is used in contexts where the independence [of what is stated] as a condition is weak.’ (I had to add a few words in square brackets to make it flow more naturally.)
This matches what the DoBJG says about the cause or reason in S1 being ‘evident and acceptable to the hearer’, since it is ‘objective’. I presume that the idea of it being ‘valid’ also stems from that objectivity. On the other hand, から is essentially ‘subjective’, which is the reason the same ‘assumption’ doesn’t apply.
Given that the condition expressed by ので tends to be less ‘independent’, we could perhaps say that the second half receives more emphasis. My way of seeing it is that the causal relationship is more natural and evident for ので, and that S1 and S2 tend to form a sort of block. This idea of ‘natural causation’ is fairly common as a nuance in Japanese, and is also among the use conditions for conditional structures such as 〜ば and 〜と. I am not certain about the question of emphasis, but perhaps it does not in fact come into play, or is at least secondary in importance to the types of causes or reasons expressed.
