So can be used to say that another subject is doing something "as well" or "in addition." - you can keep things in one sentence with so but not with as well or in addition (so that's why it happens in speech often):
Vinay plays cricket, and so does Ashok.
Vinay plays cricket. Ashok does as well.
But if there's a second action, so takes on the meaning of because of that:
He can speak French, and so can speak German.
He can speak French and because of that he can speak German.
Don't use so at all, simply say
He can speak French and German.
The problem with this:
I seldom went to Christmas parties, neither did he.
is that while "seldom went" has the meaning does not go that often, it's not a verb in negative form, so neither doesn't correctly link back to it.
You can either change "seldom went" to a negative verb, add "he" to the subject of the sentence, or make "neither did he" a full sentence with "either". ("Seldom" is one of those words you generally don't want to overuse by using it in two sentences in a row.)
I didn't tend to go to Christmas parties, neither did he.
He and I seldom went to Christmas parties.
I seldom went to Christmas parties. He didn't usually show up to them either.
There is no clean way to parse "More important, ..." strictly as written, but the intent is easy to understand.
A critical point is in the answer you reference:
...the adverbial phrase ‘more importantly’ modifies nothing in the sentence. What is wanted in constructions of this kind is ‘more important,’ an ellipsis of the phrase ‘what is more important.’
(Note that this is a subject with some disagreement, and the above quote expresses one opinion (of many) in the debate.)
If we accept that "More important, ..." is short for "What is more important is that..." then there is no issue at all: important modifies the fact expressed in the that clause.
Consider the following similar sentences:
Finding the treasure is important.
It is important that we find the treasure. (using an expletive it)
If we ask "What is important?" the answer is "that we find the treasure". (Or, "finding the treasure" in the first setence.)
You can also read "More important, ..." simply as:
This fact is more important: ...
"More importantly, ..." doesn't usually modify a verb in the main clause:
We lost the the treasure. More importantly, we lost our friends in the woods.
You didn't importantly lose your friends -- that doesn't make too much sense. Rather, you lost your friends, and that fact is more important than the fact about the treasure.
Best Answer
Yes, the construction "so"+adverb+adjective is so perfectly fine, that you can use it to really drive home the adjective
One does need to be aware of heaping superlative upon superlative