Wif and I had decide to go ahead and replace the old fence entirely instead of just replacing one post and repairing the two fallen sections. Some of the main reasons were that the previous people who put in the fence did some really odd spacing on the posts and they also only did 5 foot boards instead of 6 foot. We do have a slope across the back that would place the side on the right about 6-8" higher than where it ends up on the left but we are going to try and maintain six foot height all the way across and do the step down behind our shed.
The taller fence will make so we see less of the neighbors delipidated shed and maybe a bit less of their backyard door (and messy yard). Our contractor already removed the old fence today. He was drilling out the post holes today and trying to set the posts, then concrete them in for tomorrow.
A couple older pics to show where the 5' tall fence ends up. The fence on the right side of the property is a 6' tall we had installed already. If you look closely you can tell it is noticeably taller than the fence along the back... that 1 foot makes a difference.