So I was able to put together a fix by looping through each form.
// Fires when an Ajax form submission has completed successfully, and mail has been sent.
document.querySelectorAll('form.wpcf7-form').forEach(function(form) {
form.addEventListener('wpcf7mailsent', function(event) {
// Get input type file element
var inputFile = form.querySelectorAll('.wpcf7-drag-n-drop-file');
var status = form.querySelectorAll('.dnd-upload-status');
var counter = form.querySelector('.dnd-upload-counter span');
var error = form.querySelectorAll('span.has-error-msg');
// Reset upload list for multiple fields
if (inputFile.length > 0) {
inputFile.forEach(function(input) {
localStorage.setItem(input.getAttribute('data-name') + '_count_files', 1); // Reset file counts
});
} else {
// Reset file counts
localStorage.setItem(inputFile[0].getAttribute('data-name') + '_count_files', 1);
}
// Remove status / progress bar
if (status) {
status.forEach(function(statEl) {
statEl.remove();
});
}
if (counter) {
counter.textContent = '0';
}
if (error) {
error.forEach(function(errEl) {
errEl.remove();
});
}
}, false);
});