To follow up for posterity, I ended up using DHL. Once I received the tracking number, I signed up for shipment notifications with my phone and email address. When the package arrived in Bangkok, I received a link with the customs fees which were about 10% of the declared value, so it's possible they increased the declared value and that was 7% of their calculation. I didn't receive any breakdown of the calculation, just a flat fee I needed to pay.
I used the link and paid the fee, and the package was delivered the same day to my condo.
I think as @BMW Overlander mentioned, DHL has in-house customs, which I think did help smooth the process. The duties weren't too outrageous either.