Fourth Suit After a Reverse

One of my friends recently sent me an email with this hand:
Axxx Kxx 9x Kxxx
His partner opened 1 Diamond, he responded 1 Spade and his partner rebid 2 Hearts. What do you do with this hand? What methods do you like to play in this situation?

My favorite methods after a reverse include the Lebensohl convention where a bid of 2NT is artificial, generally leading to a sign-off in one of opener's suits at the 3-level. A rebid of responder's suit at the 2 level shows at least 5 card length, is ambiguous in strength and forces for one round. Then direct 3-level bids in opener's suits are forward-going, game forcing. A 3NT bid should show a fair hand with no fit--on the given auction, something along the lines of KQTx xxx xx KQTx. I suppose that Lebensohl followed by 3NT should show something as well...maybe a doubtful 3 No bid like KTxx Qxx xx KJxx--I don't think that I've discussed that in any of my partnerships though. Getting even more off of firm ground, what does the 4th suit mean? I guess absent any discussion it is natural--certainly possible. Give responder Qxxx Qx xx AKxxx and that meaning works pretty well. To me that hand is too infrequent--call the 4th suit a game-force not quite fitting with a textbook bid--a hand that needs more information about opener's hand. That seems to fit for the example hand--with two very useful cards for partner (contrast this hand, with the ace of spades and king of hearts, to the example hand which was worth only a direct 3NT) but no known 8 card fit, you can start with 3 Clubs. In this instance you'll get a 3 Diamond rebid from partner and know at a reasonably low level that he is 6-4 and will at least be better placed to evaluate best game/slam prospects. Partner's hand was:
Kx AQxx KQJxxx A