Usage of sentence-initial besides in English

I've read a lot of papers written by Taiwanese in English. Most of the writers have a master's degree or a doctorate, and some the writing is impressive. But no matter how good the writing, one things that bothers me about the writing of almost all Taiwanese is the non-idiomatic usage of the word "besides." It is used to begin a sentence, followed by a comma, and it is used synonymously with "in addition" or "also."

Judging by my ear, this is not a correct usage. However, checking the dictionary, it appears to be ok. See these examples:

Besides is an adverb or preposition that means "also, additionally": I would enjoy going on a vacation besides.

And from Wiktionary:

1. also; in addition
2. moreover; furthermore

But let's take a look at how besides is actually used in English writing when it starts a sentence followed by a comma. These examples are randomly selected from an English corpus.

Maybe he should have kept in touch. Gone back for reunions. But he had
been busy building a business, being a big man in his own town just as he
had been a big man at Hanford, Class of 1935. Besides, Cady Partlow
knew he wasn't the old-grad-type.

Used to further argue against the proposition that he should have kept in touch.

Who, then, is of sufficient stature to lodge with Lenin? Who but Nikita
himself? Since he has just shown who is top dog, he may not be ready to
receive this highest honor in the gift of the Soviet people. Besides,
he can hardly avoid musing on the instability of death which, what with
exhumations and rehabilitations, seems to match that of life.

Used to further argue against the proposition that Nikita is ready to receive this highest honor.

"Aren't you sure"? I asked, looking at her searchingly. I wanted to
grab her by the arm and beg her to wait, to consider, to know for certain
because life is so long and marriage is so important. But if she were
just having a normal case of pre-nuptial jitters such a question might
frighten her out of a really good marriage. Besides, in all honesty, I
don't know how you can be sure.

Used to further argue against asking the question.

I want you to find Monsieur Prieur at once and give him this money for the
boy's purchase. There's $600 in gold in this chamois sack. If the old
fool argues about the price, tell him I shall order my husband not to treat
him as a patient any longer. Prieur has gout and depends on Louis' pills
and bleedings. Besides, he owns 300 slaves. One less shouldn't
matter to him".

Used to further argue that he should not haggle over price.

We don't need this type of protection any more. The public is now armed
with sophistication and numerous competing media. Besides, there are no
longer enough corruptible journalists about.

Used to further argue against the need for this type of protection.

Auditors were encouraged. In the regular sections they have always been
more or less discouraged. The philosophy has been that if they could find
the time to attend class why not encourage them to get the credit and
perhaps provide an incentive to do the work more effectively. Besides,
auditors do not count on faculty load with the same weight as regularly
enrolled students. But in this one section we welcomed auditors.

Used to further argue against the practice of auditing.

Both these youths, who greatly admired Henrietta, were somewhat younger
than she, as were also the neighboring Friedenwald boys, who were then
studying medicine and bright though they all were, they could not possibly
compete for her interest with Papa, whose mind- although he never tried to
dazzle or patronize lesser lights with it- naturally eclipsed theirs and
made them seem to her even younger than they were. Besides, Miss
Henrietta- as she was generally known since she had put up her hair with a
chignon in the back- had little time to spare them from her teaching and
writing so Cyrus Adler became interested in her friend Racie Friedenwald,
and Joe Jastrow- the only young man who when he wrote had the temerity to
address her as Henrietta, and signed himself Joe- fell in love with pretty
sister Rachel.

Further argues that the boys could not compete for her interests.

In the course of our talk, Askington mentioned that he spent part of each
week studying. "By yourself"? I asked. "No, I take classes with
different people", he said. "I don't think I've reached the point, yet,
where I can say I know everything I ought to know about the craft.
Besides, it's important to the way a painter thinks that he should move in
a certain atmosphere, an atmosphere in which he may absorb the ideas of
other masters, as Du^rer went to Italy to meet Bellini and Mantegna".

Further argument against studying by himself.

Macneff smiled and said, "I am glad that your scriptural lessons have left
such an impression". How could they not? thought Hal. Besides, they
were not the only impressions. I still bear scars on my back where
Pornsen, my gapt, whipped me because I had not learned my lessons well
enough. He was a good impresser, that Pornsen.

This usage is a little different from the others, but maybe it can be seen as being a further argument against the proposition that Pornsen's lessons left no major impression.

* * * * * * * * * * * * * * * * * * * *

So it appears that "besides" is used in this way (at the beginning of a sentence, followed by a comma) when the author is making an additional argument against something. None of the examples are simply adding further exposition or explanation of a topic. (Besides seems to literally mean that the additional item is of secondary importance, but I don't think that is necessarily so. It can be of secondary importance or it can be of greater importance--a further point that renders the first point of secondary importance.)