What can be received on a 6 foot dish will vary from location to location. You will receive many answers, but they won't likely apply to you and your equipment. It is dependent on the dish build quality, the type of feedhorn/LNB(f), length and quality of coax, sensitivity of receiver, local terrestrial interference, footprint of adjacent satellites for your area, etc. You could get great results from one location and bad results from a different location. Why?
The problem with the question, what is the smallest dish I can use is that the size of the reflector suggested by these footprint map sites have nothing to do with reality! These maps dish size prediction is based on an assumption that you are wishing to receive a full bandwidth transponder, operated at full power under optimum conditions.
Could you use the smaller reflector to receive a full transponder operating at full power with low FEC? Yes, but it isn't only about how much signal is collected by the surface area.
Anything smaller than an 8 foot reflector on C-band and the beam width is too wide and it will pick-up signals from nearby satellites. This will introduce interference that will degrade the reception. Most transponders do not use the full bandwidth. Most transponders are not operated at full power. Most transponders do not transmit at low FEC. Many channels are transitioning to DVBS2 format which requires a larger dish for reliable reception.
Buy a 8' or larger dish. It will provide reliable reception on most of the available channels. Buy a smaller dish and your results will vary.