Roth conversions such as this are not involved in the once-per-12-months rollover limitation. Only traditional IRA-to-traditional IRA and Roth IRA-to-Roth IRA rollovers are involved in this limitation.
With regard to making a separate Roth IRA contribution, the amount converted to a Roth IRA ($40,000 if the entire $40,000 ends up in the Roth IRA) is subtracted from AGI when determining your MAGI for this purpose. In other words, the amount converted to a Roth IRA has no impact on the amount that you are separately eligible to contribute to a Roth IRA.
