There can be some weird situations where, if you are underpaid, the IRS can back-calculate the penalty based on spreading out the extra income over the whole year. But, if you are caught up and don't owe when you file, that situation should never come up. So I would make sure to pay slightly more than you think you will owe, as you would get the extra back as a tax refund. Tax for a conversion done from June-August would be due Sept 15; tax for a conversion done after August 31 would be due January 15.
I can't think of any particular harm or benefit to making several smaller conversions or one large conversion, unless you have concerns about having the funds available to pay the estimated taxes.
Don't forget you likely will owe estimated state tax payments as well.
