Split the states up:
https://screencast.com/t/fWIZ5oDqNZ

Each state:
https://screencast.com/t/VIvtKErBi

Here’s the code under piklist/parts/settings/changelog.php

<?php
/*
Setting: reciprocity_changelog
Order: 1
 */

use \App\Model\ReciprocityData;
use \App\Model\ReciprocityStates;

$selectedState = $_GET['state'];
$states = ReciprocityStates::getStates();

/**
 * SECTION 1: CHOOSE A STATE
 */

if (!$selectedState || empty($selectedState)):
?>

<h1>Choose A State</h1>

<div class="state-selector">
	<?php foreach ($states as $state): ?>
		<?php $stateAbbreviation = ReciprocityStates::getLowercaseStateAbbreviation($state);?>
		<a href="<?=admin_url('edit.php?post_type=reciprocity-pages&page=changelog&state=' . $stateAbbreviation)?>" class="state-selector__option"><?=$state?></a>
	<?php endforeach?>
</div>
<style>
	.state-selector {
		columns: 4;
	}

	.state-selector__option {
		display: block;
		font-size: 1.5em;
		line-height: 2;
	}

	#submit {
		display: none;
	}
</style>

<?php
/**
 * SECTION 2: STATE IS CHOSEN SO SHOW UPDATES
 */
else:
	$selectedStateName = ReciprocityStates::getStateNameFromAbbreviation($selectedState);
	$updates = ReciprocityData::getReciprocityUpdates($selectedStateName);
?>

<h1><?=$selectedStateName?> Changelog</h1>

<p class="changelog-note">Changelog descriptions allow Markdown, which allow links in the following format:<br><code>Read the [blog post](https://www.usconcealedcarry.com/link-to-blog-post).</code></p>

<div class="new_log">
	<p>Fill out the fields below and click "Add Update" to add a new update.</p>

	<div class="field-row">
		<label class="field">
			<span class="field-label">Date</span>
			<input type="date" name="reciprocity_changelog[<?=$selectedStateName?>][<?=count($updates)?>][date]" class="field-input">
		</label>
		<label class="field field--wide">
			<span class="field-label">Description</span>
			<input type="text" name="reciprocity_changelog[<?=$selectedStateName?>][<?=count($updates)?>][description]" class="field-input description-field">
		</label>
	</div>

	<button type="submit" name="submit" id="submit" class="button button-primary">Add Update</button>
</div>

<?php
foreach ($updates as $i => $update): ?>
	<div class="field-row">
		<label class="field">
			<span class="field-label">Date</span>
			<input type="date" name="reciprocity_changelog[<?=$selectedStateName?>][<?=$i?>][date]" value="<?=$update['date']?>" class="field-input">
		</label>
		<label class="field field--wide">
			<span class="field-label">Description</span>
			<input type="text" name="reciprocity_changelog[<?=$selectedStateName?>][<?=$i?>][description]" value="<?=$update['description']?>" class="field-input description-field">
		</label>
	</div>
<?php endforeach?>

<style>
	.changelog-note {
		background: #def;
		border: 1px solid #69b;
		border-radius: 5px;
		padding: 15px;
	}

	.new_log {
		background: #fafafa;
		border: 1px solid #ddd;
		border-radius: 5px;
		padding: 15px;
		margin: 15px 0;
	}

	.field-row {
		font-size: 16px;
		display: flex;
		padding-bottom: 15px;
	}

	.field {
		flex: 1;
		padding-right: 15px;
	}

	.field:last-child {
		padding-right: 0;
	}

	.field--wide {
		flex-grow: 5;
	}

	.field-label {
		font-weight: bold;
		display: block;
		padding-bottom: 5px;
		padding-left: 5px;
	}

	.field-input {
		font-size: inherit;
		height: 2em !important;
		padding-left: 10px !important;
		padding-right: 10px !important;
		width: 100%;
		line-height: inherit !important;
	}

	.description-field {
		min-width: 500px;
	}
</style>

<?php endif?>

<!-- STYLES FOR BOTH SECTIONS -->
<style>
	#wpbody-content h2 {
		display: none;
	}
</style>

And the pre_update_option_xx filter:

function changelogUpdateFilter($new, $old) {
	// Remove Piklist's default filter. It doesn't work for our needs.
	remove_filter('pre_update_option_reciprocity_changelog', array('piklist_setting', 'pre_update_option'), 10);

	$returnVal = $old;

	foreach ($new as $state => $updates) {
		// Filter out "Empty" results (submitted form without adding a new entry)
		$updates = array_filter($updates, function ($update) {
			return !empty($update['date']) && !empty($update['description']);
		});

		// Make sure the updates are in new->old order
		usort($updates, function ($a, $b) {
			$a = $a['date'];
			$b = $b['date'];

			if ($a == $b) {
				return 0;
			}
			return ($a > $b) ? -1 : 1;
		});

		// Add new entries to the rest of the changelog by replacing all of the state's update with what was submitted,
		// since previous updates to that state are included in the form submission.
		$returnVal[$state] = $updates;
	}

	return $returnVal;
}

Nevermind. I figured it out (I believe. I haven’t actually finished fixing it and testing to see it work). Turns out it wasn’t working with the Piklist version either. With so many entries, I was running up against the POST request size limit for my server, so the data was getting truncated. The truncation was causing it to fail validation so Piklist was saying to use the old value.