Why does my request-promise function work in Chrome but not Firefox or Safari?

Question

I'm trying to use a script for a webpage that scrapes and then parses an RSS feed using request-promise. From what I understand, request-promise has to run server-side, so I'm calling the script externally in my html. I've been using localStorage.setItem and localStorage.getItem to pass the variables between the external script and another embedded script that assigns the variables to html elements that should be displayed throughout the page as text.

In Chrome, when the page first loads, it's blank, but then works fine after I refresh it once. In Firefox and Safari, it remains blank no matter how many times I refresh. The issue seems to be that the html is not "receiving" the variables from localStorage.getItem. I suspect it has something to do with the way the different browsers are handling the request-promise function, but I'm stumped. What am I doing wrong?

Here's the request-promise script:

var xmltext
var latlonquery, latquery, lonquery, url

const rp = require('request-promise')
const options = {
            headers: {'user-agent': 'node.js'}
}

function doQuery() {
    latlonquery = new URLSearchParams(window.location.search)
    latquery = latlonquery.get("lat")
    lonquery = latlonquery.get("lon")
    url = "https://forecast.weather.gov/MapClick.php?lat=" + latquery + "&lon=" + lonquery + "&FcstType=digitalDWML"
}

function doRequest() {
return rp(url,options).then(function(html){
  return html
  })
}

doQuery()
doRequest().then(function(html){
                 xmltext = html
                 localStorage.setItem("xml_says_this", xmltext)
                 localStorage.setItem("lat_says_this", latquery)
                 localStorage.setItem("lon_says_this", lonquery)
})

You can see an example of the problem in action here.