Only 3 5x7 sheets, and 3 8x10 sheets to get one 8x10 right? Seems like a lot less paper than I use getting to a final print! After test strips, it's usually 4 or 5 sheets just to get close, then starts the fine adjustments.
That said, since you have the dodging and burning and contrast already "in the ballpark," you should not have to make too many 16y20s to get where you want.
However you need to use your enlarger to get a 16x20, the head will be farther from the baseboard and the enlarging exposure appropriately more (inverse square law ... can't break it!)
Use the 4x enlargment factor as a starting point, keeping in mind that larger prints often need a bit different contrast (you may want to tweak that a bit). Think of your dodging and burning as percentages of the total exposure and scale them up to fit your new print size (you may want to tweak them a bit too).
Don't be afraid to use some paper to get a print you are happy with! The best tool in your darkroom is the trash can!