Don't forget the lowly astronomer working at one of the observatories in the Atacama Desert, or one of the many indigenous peoples who preceded those astronomers. The combination of high altitude and latitude near the Tropic of Capricorn makes these people well-sited for being the Earth-bound people who are both closest to and furthest from the Sun at various times of the year.
With regard to closest to the Sun, that would go to one of the astronauts on Apollo 8. With regard to furthest from the Sun, the Apollo missions are out of the question. A good candidate is some unnamed person near San Pedro de Atacama, Chile on July 4, 1731.
The primary constraint of the Apollo missions was to have the Sun at an inclination of five to twenty degrees at the landing site at the time of landing. An inclination lower than five degrees made for too many shadows, while an inclination higher than twenty degrees made for too few shadows. This meant the Sun had just risen or was about to set at the landing site. A setting Sun would not have worked for the rest of the mission. Landing was performed just after the Sun had risen, and that meant that lunar orbit insertion occurred with the Moon in waxing crescent. At waxing crescent, the Moon is closer to the Sun than is the Earth but is swinging away from the Sun. Departure took place a few days later, with the Moon at first quarter or waxing gibbous.
This bodes well for an Apollo astronaut being the person closest to the Sun, but bodes ill for an Apollo astronaut being the person furthest from the Sun. For closest to the Sun, we need to look for a mission in December or January. That would be Apollo 8 and Apollo 14. Apollo 14 made it's lunar insertion a month after perihelion. Apollo 8 made it's lunar insertion a bit over a week before perihelion. Apollo 8 is the winner in this regard. The closest point to the Sun would have occurred about 20 minutes after lunar insertion. Which of the three Apollo 8 astronauts was closest to the Sun? Who knows. They were quite busy at that time.
With regard to furthest from the Sun, the Apollo missions closest to aphelion (early July) were Apollo 11 and Apollo 15. The combination of departure time (in terms of lunar phase) and departure date (in terms of closeness to aphelion) means the Atacama Desert dweller on July third or fourth will have been further from the Sun than those astronauts were at their furthest points from the Sun.
Perhap a vehicle in low Earth orbit? Whether the astronomer or astronaut is further from the Sun depends on solar beta angle. The solar beta angle needs to be between -20 and +20 degrees for the astronaut to be further from the Sun than the astronomer. Next, we need to look to the Moon on July 4. A new moon is ideal, a full moon, the opposite. New moon versus full moon makes for a swing of over 9000 km in distance between the Earth and the Sun. There have only been a few new moons in early July during the space age. To find an astronomer who was further from the Sun than an Earthbound person, you need to find a populated vehicle whose beta angle was close to zero at one of those few times when the moon was new at aphelion.
Not all new moons are created equal. The Moon's orbit is eccentric and is tilted with respect to the ecliptic and to the equator. An annular eclipse on July fourth over southern China is just about perfect for making a person in San Pedro de Atacama be furthest from the Sun. One candidate, as mentioned above, is July 4, 1731. I'm sure there are even better ones further in the past.
Update: How I arrived at this answer
My primary tool for verifying what I wrote was JPL's Horizons system. With this, I was able to verify that there is no way anyone has been closer to the Sun than the Apollo 8 astronauts and that there is no way anyone has been further from the Sun than some unnamed person near San Pedro de Atacama, Chile on July 4, 1731.
The website StarDate Online shows the phases of the Moon for any month since 1951. New moons very close to July 4 are needed to make a spot on the Earth, or in low Earth orbit, qualify as furthest from the Sun. The only years where this happened in the space age were 1962, 1967, 1970, 1978, 1981, 1989, 1992, 1997, 2000, and 2008. I checked all of them. None were anywhere close to the distance achieved on July 4, 1731. That was a red letter date.
What made me choose that date? Wikipedia has extensive lists of total solar eclipses, dating from the 20th century BCE to the 30th century CE. I was looking for an annular eclipse late June / early in July that occurred at around 23 north latitude, 110 east longitude.
Why that search? The Moon's orbit is inclined by about five degrees with respect to the ecliptic. A solar eclipse occurs when the Earth, Moon, and Sun are perfectly aligned, which increases the distance between the Sun and Earth over nominal separation at new Moon. An annular eclipse means the Moon is abnormally far from the Earth, which in turn means the Earth is abnormally far from the Sun. The target latitude/longitude are diametrically opposed to my chosen point of San Pedro de Atacama. Why San Pedro de Atacama? The Andes are without parallel in the southern hemisphere. They make the tallest peaks in southern Africa and northern Australia look like hills.
There were no good candidates this century, nor in the 20th century, nor in the 19th century. But then bingo! July 4, 1731 was almost perfect. On testing that date with Horizons, it was clear that no one has been further from the Sun since that date, including the Apollo astronauts, or any cosmonauts or astronauts in low Earth orbit. The Apollo astronauts who ventured furthest from the Sun were those on Apollo 11. (Apollo 15 was a close second.) An astronaut or cosmonaut in low Earth orbit on July 4, 2008 was considerably further from the Sun than those Apollo 11 astronauts. My unnamed person near San Pedro de Atacama was in turn considerably further from the Sun than those astronauts and cosmonauts on July 4, 2008, by over eight thousand kilometers.
Certainly there is some date even further in the past with an annular eclipse that occurs even closer to the nominal aphelion passage date and even closer to the target latitude / longitude than the date I found. The date I found was good enough to show that it was ordinary Earth-bound people rather than astronauts or cosmonauts who have been furthest from the Sun.