I will enter on TR soon and plan to extend for 30 days. After the extension period I will need another 28 days so will there be an issue to exit (Laos or Cambodia) and immediately return with exemption. I am USA.

One wrinkle is I am dual-nat Thai. Someone told me I could just forget the TR and enter with Thai passport and leave with USA one. But, I will be renewing my Thai passport while in Thailand; I am concerned I might lose my record of entry and cause problems. Any assistance will be appreciated.

Yes, you should enter Thailand with your Thai passport. Getting any kind of visa etc denies your natural and legal status.

After you renew your passport you may need to show the old one when leaving, if asked. The record of entry is never lost, it's in immigration database.

Since you will be entering as a Thai you do not need a record of entry into the country because you can stay for infinity.

When you leave the country just show your new Thai passport to immigration.

Enter and leave on your Thai passport, you will give in your tm6 arrival card, which you should have with you now in your passport, and then start a new tm6 departure card when you leave with your new passport