According to Wiki, Nostradamus claimed to have used judicial astrology to make his predictions, I find that doubtful, not that he said it, but that he used it. Astrology is broadly divided into two groups, judicial and natural. Natural astrology is the use of astrology to predict weather and natural events like earthquakes, floods etc. Some might include mundane astrology in this group, the rise and fall of kingdoms. Like I said the terms are very broad. Judicial astrology includes what most of us know as astrology, horary, natal and again some include mundane here rather than in natural astrology. St. Thomas Aquinas apparently had no problem with natural astrology and in Nostradamus time he would not have been persecuted for practicing astrology since he was a physician and this was part and parcel of the physicians education.
Nostradamus was criticized for using astrology the way he allegedly did: comparing future planetary alignments with past alignments and the events that were associated with them. Without knowledge of the 3 outer planets this would be difficult, but not impossible with tables and mathematical ability.
This method is used by contemporary astrologers, and in fact is what very early astrology is based upon. To my knowledge Nostradamus left only those quatrains and not the methodology used.
Then there is the problem of the quatrains themselves. If in fact he used astrology there was no reason to hide his predictions behind ambiguous phrases. The Wiki article claims fear of the Inquisition, but that is unlikely and it only demonstrates that the Wiki authors know little about the true nature of the Inquisition and have simply jumped on the popular history bandwagon. Most importantly, he would not have been investigated for heresy for using astrology. Magic is another matter. So the Wiki article implies he used magic and claimed astrology to keep himself out of trouble with authorities.
If he used astrology, it would have been Western Tropical, possibly influenced by Guido Bonatti (?- 1296-1300?) and Ptolemy (2nd century AD). It is doubtful he would have known about the others you listed.
The quatrains themselves are of obscure meaning and lend themselves to "after the fact" prophecy. They are an historical curiosity and of little value to astrologers.