You will need to be flexible when planning a trip on the upper Buffalo in advance. Water levels are not a given. If you look at historical discharge data for the Ponca USGS gauge, daily mean flows for the period March 15 - March 30 averaged over the last 8-9 years are anywhere from 234 cfs to 818 cfs. Remember, these are mean flows for an 8 year period, so in any given year the flow for the particular date may have been considerably lower or higher than that.
Two hundred thirty four cfs is pretty low for putting in at Ponca, especially if you are paddling a loaded tandem canoe. Over 800 cfs is pretty high and may be above your comfort level. There is at least one Class II rapid between Ponca and Kyle’s Landing, and at higher water it might be Class III and multiple other rapids will rate Class II. So you will need to check gauge levels as your planned departure date approaches and may need to shift to another river or a lower stretch of the Buffalo if levels are not suitable.
Last year there was an enormous spring flood in the area, and a group of three canoe campers were caught on an island during rapidly rising water, a little above Kyle’s Landing. Two of the paddlers swam, lost gear and boats, and one drowned when they tried to paddle off. They recovered the body during our last spring Rendezvous just upstream of Erbie. So pay close attention to the weather reports, and avoid camping on islands or any site from which there is not a clear escape route to higher ground.
Assuming that the water level is good, Ponca to Carver would definitely be the most scenic stretch. Check the park map:
Clearly, the shuttles to access points below Carver become significantly more painful. If you plan to use one and plan to use an outfitter to shuttle, you need to be sure that they would be willing to do so and what they would charge. Setting up your shuttle could take the better part of a full day.
I agree that four days to paddle Ponca to Carver would be rather painfully slow. I think Three days and two nights is more reasonable, allowing time to set up the shuttle the first day, and allowing you to get off the river at a comfortable time the third day. If Ponca if running, you will surely be sharing the river with others. The crowd will likely thin out significantly below Kyle’s Landing.