After a day of searching, I wasn't able to come up with an easy answer, so I implemented a work-around. I wrapped my Lightning component in a VisualForce page and overrode the content source for the New and Edit actions to use the new host page. Using Lightning within a VisualForce page takes some work. See the link below to get started.
Use Lightning Components in Visualforce Pages
Here's the code I wrote to get things working. One issue I'm still researching is getting the force:* events (ex: force:showToast and force:navigateToObjectHome) to fire correctly. I added them as a dependency with no luck.
Host.page
<apex:page standardcontroller="CallReport__c">
<!-- This page is a host page for the call report lightning component. -->
<apex:includeLightning />
<div class="slds">
<div class="slds-grid slds-grid--align-center slds-p-around--small">
<div class="slds-large-size--3-of-12"></div>
<div class="slds-size--1-of-1 slds-large-size--6-of-12">
<div id="callReport"></div>
</div>
<div class="slds-large-size--3-of-12"></div>
</div>
</div>
<script>
var recordId = '{!callreport__c.id}';
// c:callReport implements force:hasRecordId and requires the call report ID
$Lightning.use("c:DepApp", function() {
$Lightning.createComponent('c:callReport',
{ recordId : recordId },
'callReport',
function(cmp) {
// do some stuff
});
});
</script>
</apex:page>
DepApp.app
<aura:application access="GLOBAL" extends="ltng:outApp">
<aura:dependency resource="c:callReport"/>
<aura:dependency resource="markup://force:*" type="EVENT"/>
</aura:application>