Preroll a lot of stuff
I haven't run this particular module, but I have used hexcrawl and pointcrawl style play in my home campaign.
Even if I don't know exactly which way the party is going to go at any given time, I find it often useful to preroll things that I'm pretty sure are going to need to be randomly generated. I can sit at my desk during prep time and roll up 60 days of weather in advance. I'll generate 60 days worth of random encounters (and if there's different encounter tables for different hexes or times of day, I'll roll up 20 or so encounters for each environment and just pull the next one off the appropriate list when they hit the next encounter), and so on.
And then I nudge it to make little stories or conceptual plots. Random generation often comes up with just a lot of stuff-that-happens with no real coherent order to it, but with a few nudges you can turn it into something meaningful. For example, if I roll two rain days, then a sunny day, then rain, then partial rain, I'll rework it to give them three days of torrential rains, then the next day the rain breaks and it's sunny afterward. I'll often reshuffle or outright reroll random encounters when they don't seem quite thematic enough -- a series of clashes with a specific group suggests that the party is traveling through that group's land (wherever it happens to be on the map!) and that makes a better story than just running into yuan-ti four times across five weeks or something.
Skip over the boring bits
Once you know when the next random encounter is "scheduled" for and don't have to roll a bunch of dice every thirty seconds, you can move a lot faster on the day to day travel. Let the players pick a few hexes and roll their navigation without pausing too much, just give them some setting descriptions as they move along, then at the appropriate time you say "On the fourth night, as you're setting up camp, you hear a sound in the bushes--" and move along.
But remember that the journey is the story
Remember that these encounters aren't there just to be a source of XP. Emphasize how each encounter reveals the land they're traveling through. (This becomes much easier when you pre-roll your encounters and can spend time ahead to think about how they might function to show off Chult!) Consider the environment each encounter happens in and how it shows off the land -- an ancient ruin infested by a troop of aggressive baboons or a dry river bed where a massive snake sleeps say something about the territory and the kinds of people who live there (or don't).
If you look at a hexcrawl as a slow, complicated way to get from A to B to C, then yes, it's going to suck. It isn't the Indiana Jones Red Line to Adventure.
A hexcrawl has more in common with the Lord of the Rings; the land is a character in its own right, and the hexcrawl is a series of conversations with that character. As you roll up the hexcrawl, you are asking Chult, "What do you want to show me today? What are you trying to tell me?"
If you ignore the answers, it's going to feel pretty pointless.