mundi  uses a word 
(the Targums   and also some time line for that  
core of Quranic texts  1/ The article on the meaning of the word " Islam", shows the author(s) were familiar with the rabbinic writings. Can that have been expected of a Christian writer? Those books (the Targums etc) were not available outside of certain Jewish milieus. That does narrow down who wrote the texts.
dear mundi.,  I didn't get your point on coupling Quran and Islam with that word  
"the Targums". but those  Targum books/manual's ..whatever ... DO THEY MENTION THE WORD ISLAM?? OR Muhammad in them ?? 
as far as that ....... 
" the Targums were not available outside of certain Jewish milieus.  ".......    is concerned., we must realize that during 1st  to 6th century ....the Jewish folks in various sects and denominations were living all over the place from Syria, Armenia., Egypt, present Jordan, Iraq, Iran   all the way to Yemen., so those  Targums must have been present    wherever Jewish folks were living at that time.,   In fact Yemenite Jews still  use the stuff from Targums ..in their religious rituals., 
So I didn't get the reason for you to couple Targums to Quran and Islam dear mundi.,   Yes Quran has the stuff from  Targums., which is nothing but of collection  OT stories/songs sonnets  in earlier times ., almost 6-7 centuries before the birth of those so-called Quran manuscripts.,  Off curse they were not in Arabic but  in different languages such as Aramaic  or Hebrew...  good to read this book  
 The Aramaic Bible: Targums in their Historical Context  and watch this one on those good old languages of Middle East
https://www.youtube.com/watch?v=epEMncIAhjg2/ 1). For me the Quran as a book (maybe a text here or there missing) exists from before 630 (C14 proves it). 
2). Maybe not all text material was original and might even from 6th C, but the collection itself seems to have been done with the purpose of making a theological point. 
3). So no Yeez, I dont think there is a pure core of Quranic texts corrupted by some later evil doers. WYSIWYG: 
4). there is material in the book that is acceptable to us 21st C people, and there is material that is totally unacceptable.  Maybe the Quranic author(s) should not be reduced to their worst Quranic ideas? 
 Well all that what you said above is a HANDWAVING statement that will have loads of questions dear mundi., let me throw  few questions 
1). For me the Quran as a book (maybe a text here or there missing) exists from before 630 (C14 proves it).
Nope.. No...Noooooooo.,  I disagree and I doubt it.,  you got to come out with much more than one line statement to prove that dear mundi 
2). Maybe not all text material was original and might even from 6th C, but the collection itself seems to have been done with the purpose of making a theological point. 
When you say 
"might even from 6th C"  .. what does it mean ?? Part of Quran  book was floating around in the year 530??  550?? 570?? 590??     and WHAT THEOLOGICAL POINT  are you talking dear mundi?? ..  pick it up from these points..
1). There is no Allah/God   but Allah/God 
2). And Allah's last Prophet and   last messenger is Prophet Muhammad 
3). Jesus Christ is NOT God.. or Son of God .. just a messenger or  at best a prophet 
4). Allah/God can not have any kids 
5). All previous Jewish/Christian/Greek/Roman/Pagan whatever  scriptures are corrupted .. completely corrupted by their followersApart from the above so-called theological points.. what else is there in Quran As THEOLOGY dear mundi??  PLEASE ADD MORE THEOLOGY IF YOU CAN 
3). So no Yeez, I dont think there is a pure core of Quranic texts corrupted by some later evil doers. WYSIWYG:
you got to come up more than a STATEMENT to get me 
that pure core of Quranic texts dear mundi .,WHAT IS PURE CORE QURANIC TEXT??  give me some  core of Quran.,  AND WHO SAID LATER EVIL DOIERS ADDED STUFF IN TO  PURE QUARNIC STUFF?? TRUE THEY CAME UP WITH LOTS OF JUNK in HADITH .. but Quran at the 
end of 7th century .. it is already done and dusted 
4). there is material in the book that is acceptable to us 21st C people, and there is material that is totally unacceptable.  Maybe the Quranic author(s) should not be reduced to their worst Quranic ideas?
Off course there is a material in the book that is acceptable to us 21st C people., which I think was also there in 1st century .. 2nd century 5th century .,   What material from Quran you think unacceptable ?? Is it unacceptable to those follow Islam as faith strictly??
No.. Noo.. Quran is a book of its time ., it served its purpose for 7th century folks .. it served their political/economical and spiritual needs of the leaders as well as public  ., 
SO I WOULD NEVER EVER REDUCE  Quranic author(s) to their worst Quranic ideas?but now you  print me out/write to me  on  
Quranic author(s) worst Quranic ideas  with best wishes
yeezevee