125 plan year different from benefit contract renewal date

[Guest Nodak]

Company has a full cafeteria plan (125) with a plan year of 1/1 thru 12/31, all insurance contracts, but for one, renew on 1/1. Company also has a fully insured health insurance policy with a renewal date of 7/1. Insurance Company only permits election changes (absent a QE) at the time of renewal.

Employee does not elect heath insurance when first eligible, and has no qualifying events. If the employee wishes to elect health insurance for the following plan year, must the employee elect coverage prior to the start of the 125 plan year (to satisfy the 125 regs) and then wait until 7/1 for the coverage to become effective (to satisfy the health insurance contract)?

Treasury Reg 1.125 - 2 Question 6 seems to cover premium increases without issue, but what about new enrollees and/or participants changing beneficiary coverage without a QE?