Both are non-taxable transactions. What you describe for the movement of funds between Fidelity accounts would not be a distribution or rollover and is not reportable. Since it's not a rollover, it has no bearing on the one-rollover-per-12-months limitation. The movement of funds from the 401(k) to an IRA is a distribution and rollover, but rollovers from a 401(k) are disregarded with respect to the one-rollover-per-12-months limitation.
Any movement of the resulting IRAs to IRA annuities should similarly be done by trustee-to-trustee transfer to avoid any involvement of the one-rollover-per-12-months limitation because such transfers of IRAs are nonreportable.
