ThyJourney

Congrats!!  Don't forget to change your W4 (tax) to reflect this. Can be easily missed with all the immigration document preparations. 

So far looks good. I see the State Department implemented the G325 into the i-129F and of course increased the fee.  This is entirely up to you and your fiance, but how about a simple fiance ceremony with family on your next visit? or just photos with your fiance family should be suffice enough.  Good luck with your journey and be patience. 

You can have the  SSC that says "Valid for work only with DHS Authorization"  removed after she receives it if you want. All you have to do is submit your documents for AOS, EAD and AP using your last name once you get your copy of Marriage Certificate.  Since she received her GC you'll just have to resubmit the SSC application to change her last name and to change the status of the current SSC to remove the "Valid for work....".
Congratulations!!    

Here's my two cents worth:
I would not pay Sid Sod. Before doing anything both of you should read 'Thailand Fever', because it's pretty accurate. Amazon sold it cheap: https://www.amazon.com/Thailand-Fever-Chris-Pirazzi/dp/1887521488/ref=sr_1_1?ie=UTF8&qid=1501121760&sr=8-1&keywords=thai+fever
 
Next thing you should do is to take a vacation from your busy schedule and travel to Thailand and meet her in person and then meet her family. Sometimes it may not even work out and you'll both will not have to worry about anything. You have to remember before you two decide to get married there is a Engagement ceremony with small amount of money involved to pay for ceremony and little sid sod. Usually, after the Engagement ceremony the family will pick date for wedding for you two to choose and also the price for the Sid Sod will be discussed. In my opinion, you will be wasting a lot of money and you will probably will not see a penny of it after paying any amount of the traditional Sid Sod. 
Keep it simple and just do a K1 visa so she can visit the USA earlier time within a year. CR1 will take on average 14 months and might be too long for her to wait. Not sure where her  family is located, but if they are located near Bangkok this place offer good price for very good exquisite traditional ceremony. Of course, with every ceremony there is the thai traditional wear you will have to rent for yourselves and the family. http://www.rueanpranine.com/   or have ceremony at her place with her family and friends.
You mention she is nurse, right?  My wife is a nurse as well and is prepping for the board exam and licensing in USA. They will still need to prep for the certification board exam. Reason i mention this is because if she is here on CR1 after you two married there in Thailand. She could change her mind and leave you. Living in the USA is not what most think it is and most thai are cultural shock, home sick, lonely, etc. and will expect to travel back home to leave USA for good.
meaning you just lost  the entire Sid Sod and you will still be responsible for her expenses as stated in the Affidavit Support. 
With a K1 visa, she is here and if she wants to stay then your all good to go. You'll have extra money for making family, new house, etc....  You will not with Sid Sod. 
 
 
 

Thing is that you are obligated to "Affidavit of Support" until she reaches 40 qualifying quarters of work or she becomes US citizen or she is not LPR anymore.
She is LPR until she legally surrender her GC or USCIS decides she is no more LPR.
In my opinion, you guys are in good term so you don't have to worry much about it. To be rest assured, you can convince her to come to US embassy or consulate in Thailand to legally surrender her GC.

That is why I suggested notifying the uscis that she no longer lives in the US. You are obligated whether you are married or divorced. She has to surrender her greencard or become a USC or complete 40 quarters.

Just inform the USCIS that she has moved back to her country and has no desire to have the green card. They will assume she abandoned her residency. Put it in writing and call. That will also remove your affidavit of support obligation.