The Premiere Customer Support team was able to help me out.  As it turns out, there's a couple of hoops you need to jump through to make this work in the context of a trigger.  Here's some sample code:

trigger PersonAccountTesterTwo on Contact (before insert, after insert) {
	// This trigger walks you through the process of converting a new Contact into a Person Account.
	// 1) The first key element in making this work is that the Contact needs to be linked to the 
	//		target account before their record types are changed. This code handles this by 
	//  	associating the Account and Contact in "before insert".  After the "before insert" 
	// 		portion of the code runs, the Account and Contact will be linked together.
	// 2) The second key element in making this work is that when you change the record type of 
	// 		the Account, you need to query for a new version of the particular Account object in 
	//  	question.   And when you query for that object, you should only query for the id of 
	//		the Account. If you were to add another attribute to the query below (like say "Name") 
	// 		the code would fail.
	// 3) Make sure to change the query for the "Person Account" record type so that it returns a 
	// 		valid record type in your org.

	// That's it!  Good luck!
	
    private static RecordType PersonAccount = [SELECT id FROM RecordType WHERE DeveloperName = 'Seeker' and sObjectType = 'Account' and ispersontype = true and isActive = true limit 1];

	if (Trigger.isBefore && Trigger.isInsert){ 
		for (Contact newContact : Trigger.new){
			Account a = new Account(Name = 'TestAccountOne');
			insert a;

			newContact.accountid = a.id;
		}
	}

	if (Trigger.isAfter && Trigger.isInsert){
		Set<sObject> ObjectsToUpdate = new Set<sObject>();
	    Map<Id, Account> AccountsMap = new Map<Id, Account>([SELECT id FROM Account WHERE id IN (SELECT AccountId FROM Contact WHERE Id IN :trigger.newMap.keySet())]);
		for (id aId : AccountsMap.keySet()){
			Account a = AccountsMap.get(aId);
			a.RecordTypeId = PersonAccount.id;
			update a;
		}
	} 
}