hardware fails after apple's repair and apple refused to take the responsibility

I have a Macbook pro 15inch late 2013 model. Except for the battery life, it worked perfectly before I sent it to apple for a battery replacement.

On this April 9, I went to apple store and asked for a battery replacement. When the repair center replaced my battery, they found issues in logic board and also replaced it for me.

Right after these replacements, I found my Macbook sometimes would shutdown without any notification. So I went to apple store again on this May 20. They did some diagnosis and suspected it was a software issue. The genius bar reinstalled the operating system for me.

After the long summer vacation, I began to use this Macbook more frequently when semester started. I saw the same issue happened again and again recently. I went to the apple store on Oct. 15 again. This time, they still does not do anything, except for a system reinstallation.

As you can imagine, the reinstallation does not help at all. Just one day after my pickup (Oct. 20), I met the same issue three times in an hour! I even took two videos that record what happened during the shutdown (see link1 and link2).

Right after this, I went to the apple store the fourth time and showed them these two videos. This time, they finally admitted that there was a hardware issue in the logic board. Because this Macbook's product life is more than 6 years now and it was out of the 3-months warranty of the initial hardware repair, they are unable to send it to apple's repair center. If I want to replace the logic board again, I have to pay over $500 to the local apple store.

I am a loyal customer of apple. I own two iphones, two ipads, two Macbooks and one iMac. I trust apple because of its great product and service. I don't want this experience ruin my trust in apple. Is there any alternative way I can seek for help?

Thanks in advance.