Checking BigCommerce plans seems they are offering "free" certificates for all their plans already, as far as I know they are using Encryption Everywhere by Symantec.
To use a certificate issued by a third party (in this case Let's Encrypt) you could do it only if you are using a Pro or Enterprise Plan.
So, I think you don't need to complicate it, just use the certificate they are offering in all their plans for "free".