The Gospels of Matthew, Mark, and Luke indicate that Jesus was crucified during 15 Nisan. This is relevant because the gospels are generally reliable, and moreover John is disinclined to overtly contradict the unanimous traditions of Mt, Mk, and Lk.
Here is the argument:
Mk 14:12-16 -- On the first day of Unleavened Bread, when the Passover lamb was being sacrificed, His disciples said to Him, "Where do You want us to go and prepare for You to eat the Passover?” […] 14and wherever he enters, say to the owner of the house, 'The Teacher says, "Where is My guest room in which I may eat the Passover with My disciples?"” […] 16The disciples went out and came to the city, and found it just as He had told them; and they prepared the Passover.
Mt 26:17-19 -- Now on the first day of Unleavened Bread the disciples came to Jesus and asked, “Where do You want us to prepare for You to eat the Passover?” 18And He said, "Go into the city to a certain man, and say to him, 'The Teacher says, “My time is near; I am to keep the Passover at your house with My disciples."'” 19The disciples did as Jesus had directed them; and they prepared the Passover.
Lk 22:7-8, 11 -- Then came the first day of Unleavened Bread on which the Passover lamb had to be sacrificed. 8And Jesus sent Peter and John, saying, “Go and prepare the Passover for us, so that we may eat it.” […] 11“And you shall say to the owner of the house, 'The Teacher says to you, “Where is the guest room in which I may eat the Passover with My disciples?'”
Jesus was crucified c. 30 AD, and it was on a Friday. This is relevant because AD 30 is the only year around that time whereby 15 Nisan (full moon) can fall on a Friday.
“The Last Supper” (Jn 13) is a Paschal meal. This is relevant because Jesus's crucifixion took place during the 24 hours following “The Last Supper” of Jn 13:2ff (i.e. 15 Nisan).
“'The Last Supper' (Jn 13) is not a Paschal meal.” This is relevant because Jn indicates that, between the Last Supper and Jesus' crucifixion, there was no time to eat another meal. Therefore, there was no time for a Paschal meal.”
“The Gospel of John indicates that Jesus was crucified on 14 Nisan. This is relevant because, trivially, 14 Nisan is not 15 Nisan.”
“Working (e.g. farming) was prohibited on 15 Nisan. This is relevant because Simon of Cyrene was coming home from working in the fields (e.g. farming) on the day Jesus was crucified.”
But, so what? Couldn't it simply be that “coming from the country” only means Simon was entering the city?
R.T. France (NT Scholar, lecturer): “His arrival ἀuγuρuw does not mean he was returning from working in the fields (it was still only mid-morning), but merely that he had been out of town and happened to meet the execution squad as he came in.” [The Gospel of Mark: A Commentary on the Greek Text (Paternoster Press, 2002) 640.]
Craig Keener (NT Hist. Jesus Scholar): “[d]evout Jewish pilgrims from throughout the Mediterranean came to Jerusalem during Passover. Roman soldiers could impress anyone into service to carry things for them. Because it is a feast and work is forbidden, Simon is not coming from “the field” (literally) as a worker; perhaps he is late for the festival, only now arriving from Cyrene or from where he is residing temporarily in the countryside. [IVP Bible Background Commentary [on Mk 15:21] (InterVarsity Press, 1993).] Elsewhere, Keener writes: “That Simon was coming in from the "field" (Mk 15:21) cannot mean that he was coming', from work - first, work was prohibited on the feast day (Lev 23:7-8) and second, one would hardly finish working in the fields at 9 a.m. The expression may thus mean that Simon had miscalculated his transportation and arrived from Cyrene late for the feast (cf. e.g., Acts 20:16; Sen. Ep. Lucil. 53.1-3; 57.1; though the most difficult travel season - cf. e.g., Acts 27:9; Jos. War 1.279-80; 2.203; 4.499; Ach. Tat 8.19.3 - had probably ended a month before); more likely, it simply means "from outside the city' (Dalman, Jesus-Jeshua, 100-1), where he had spent the night, perhaps in a nearby town.” [The Historical Jesus of the Gospels (Eerdmans, 2009) 322, fn267.]