I think that δεύτερος "second in a sequence" (connotation: others were expected to follow??), ἔσχατος "the last to be able to fit into a sequence" (connotation: it is not possible for there to be others after them??) or τελευταῖος "the last one in a sequence" (connotation: the last one of those present) could be used as an opposite for πρῶτος "first in a sequence".
In that way, reversing the order of the people in this verse;
a composiotion based on the text might be;John 20:5 wrote:Ἔτρεχον δὲ οἱ δύο ὁμοῦ· καὶ ὁ ἄλλος μαθητὴς προέδραμεν τάχιον τοῦ Πέτρου, καὶ ἦλθεν πρῶτος εἰς τὸ μνημεῖον,
If there was a need to explicate the fact that he lagged behind, then perhaps δραμὼν βράδιον τοῦ ἄλλου μαθητοῦ καθυστέρησεν ὁ Πέτρος. Using an inappropriate adverb may indicate that they ran to the tomb at different times of the day, rather than at different speeds.Ἔτρεχον δὲ οἱ δύο ὁμοῦ· καὶ ὁ Πέτρος ἔδραμεν βράδιον τοῦ ἄλλου μαθητοῦ, καὶ ἦλθεν τελευταῖος εἰς τὸ μνημεῖον,