I am not sure whether my method is useful to you,but you can try again ,i have
transfer android sms to computer in recently ,just install a transfer tools or android manager on a computer , and need a USB cable to connect the phone and computer, the app can enter the phone on the computer , it can provide a preview to you , you can select one by one before transfer ,finally , you can start to transfer , it not take your a long time to complete this task,