With regard to the 60-day rollover requirement, it's the IRS or tax court (and perhaps the receiving financial institution) that would need convincing, should they question it. From what I have read, the IRS considers the 60-day rollover window for a distribution from a 401(k) plan to begin when the funds come under the control of the employee. That happens the moment that a check made out by the plan to the employee is received by the employee and is able to be cashed. The closest reference I can come up with at the moment is PLR 201330047 in which the IRS referred to the 60-day window beginning with the date of *receipt* of a replacement check when an original check was never received.
As for proving the date that the check was actually received, there would only be your word to go on, so that would come from your sworn statement. The IRS does have some idea of the normal transit time for first-class mail.
