Since these e-documents contain no Reg. E (or other federal) disclosures, then you are (as Randy advises) concerned only with preserving the validity and enforceability of the terms of the contracts.
If this type of contract has to be "written" in order to get favorable rulings in state courts, then you need consent...but it doesn't have to be via ESIGN. Texas has a UETA, and you have the choice of UETA or ESIGN when you are e-delivering anything other than federal disclosures. UETAs are simpler than ESIGN because they require no test drive as part of the customer's consent.
Ask your attorney if Texas case law shows that UETA consent holds up in court as well as ESIGN consent. If Texas judges have a preference, that's the way to go.
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...gone fishing.