I don't think you are overthinking this, except that the "mail rule" doesn't matter for delivery purposes. You said that the "applicants never acknowledged consent or accessed the disclosures." First, they don't have have to access the disclosures (as you could assume 3 days for deliver). What they must do, however, is consent to ESIGN before you can deliver the disclosures electronically. I am assuming that you meant they did not consent to ESIGN as many systems are pretty slick and do ESIGN and delivery in one big swoop when they open the email from the lender.
If they did not consent to ESIGN, it is like you never sent the disclosures at all. Therefore, you are correct that your disclosures were not sent until day 6, violating the timing requirements. If your bank is going to be using an ESIGN system where the customer consents as part of the disclosure opening process, then your lenders (or someone) needs to watch to make sure the customer actually consents before the 3 day deadline. Otherwise, you must send them paper disclosures within the initial 3 days.
Said another way: to comply with the initial disclosure requirements, within 3 days of the application you need to either 1) have the customer consent (i.e. comply with ESIGN) and send the disclosures electronically (again they don't have to open or even acknowledge the disclosures w/in 3 days, you just have to send them) or 2) you must send paper disclosures.
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Adam Witmer, CRCM
All statements are my opinion, not those of my employer, and should not be taken as legal advice.
www.compliancecohort.com