I just went through this, but was more or less forced into accepting the lump sum payment (ouch) this year b/c Mom died intestate, and there was other legal stuff to deal with. What a mes...
Anyway, you pay taxes on any distributions from an inherited IRA like it is ordinary income. So, for me, next year's tax bill is going to be horrific.
Not sure about the additional 10% federal tax liability, unless "they" are confusing it with the 10% early withdrawal penalty. You don't get that if you cash in an inherited IRA.
Try to structure the payments so that, when added to your other income, they don't throw you up into a higher tax bracket. You'll have to get some tax software and play with the numbers here...
Personally I'd go for the periodic payment plan, but that's because my husband and I can both make a good living and we wouldn't need the money right now.