Adventures in NT Greek: Is Jesus a vegetable?

Today I’m working my way through John 6, the famous “bread of life” chapter. I noticed something curious in a section where Jesus is contrasting the “true food” of his body with the manna Moses fed the Israelites in the desert. Throughout the passage, he uses what seems to me to be the more usual verb for eat, ἐσθίω, including when referring to eating his body. But when he’s drawing a contrast, he uses a verb I hadn’t seen before, τρώγω, which appears to connote primarily the eating of vegetables, particularly by herbivorous animals — but also human “snacking” on similar light fare. Are we to graze on Jesus, presumably as a food source that’s more reliable than manna, which only lasts a single day at a time?

The LSJ does have a later meaning for the term that says it is a substitute present tense for ἐσθίω, but there’s a verse in which both appear, in what’s hard not to read as a clear and intentional contrast: οὗτός ἐστιν ὁ ἄρτος ὁ ἐζ οὐρανοῦ καταβάς, οὐ καθὼς ἔφαγον οἱ πατέρες καὶ ἀπέθανον· ὁ τρώγων τοῦτον τὸν ἄρτον ζήσει εἰς τὸν αἰῶνα (6:58; “this is the bread that comes down from heaven, not like the fathers ate and died; the one who eats this bread will live forever). Of course, there is the tense issue that the LSJ mentions….

While I’m here, I have another issue: when the disciples are gathering up the leftovers from the feeding of the 5000, the text uses the verb συνάγω. Is this meant to evoke the synagogue, and hence to symbolize gathering up the “remnant” of Israel?