Dealing with Large Wake

So I was out for lingcod over the weekend in Admiralty Inlet, and alternating between my OK Trident 15 and a 12' aluminum boat with a 6 horse kicker. I was out Saturday morning in the aluminum boat, and a large freighter passsed through the inlet. Based on the size of the wake, it was a full load. I was a hundred yards or so from shore when the waves from the wake hit, and they were very large - 10 feet or so, cresting at the top, and very close together. If I faced into the waves, even at an angle, they were steep enough that I would have plowed into the base of the next wave and gone into the drink. I turned toward the shore and basically rode them in, goosing the throttle until the wave rolled underneath me, and then rolling off the throttle until I was on the upswing again. The waves lasted for a couple of minutes, but it seemed much longer and it was a bit of an adrenaline rush (in a negative way).

After it was over, I tried to envision dealing with those in my kayak, and I couldn't picture it. If I had gone into the waves, I think they would have crashed right over me, since the valley in between the waves was so short. If I went with them towards shore, I don't think I could have kept paddling fast enough, and I feel like I would have been swamped from behind. If I caught a wave just right, it would have taken me all the way in to the rocks. Sideways would obviously be a very bad idea.

The question is, how would you deal with that situation when faced with it? The rest of the morning was dead calm, and no issues before or after the freighter. Am I not trusting the kayak enough? I'm new to kayaking so I'm not sure if I just need more experience? I grew up on the water in the area, so I'm familiar with the currents and tendencies there, although I have a healthy respect for it and never push the edge.

Before you ask, I always wear a PFD, have a drysuit when in the Sound, and have a VHF radio for emergencies.

Any thoughts/advice are appreciated. 

I put my kayak parallel to larger swells/waves and prepare to brace into it. 
Usually I just go up and over like a log would with no issue.

In my opinion it is much better to take those head-on, I've done so out there in the same area.  It is a bit intimidating, but I attacked them and paddled aggressively straight up the wake, at the top leaning forward to get the nose down the other side.  Much better to encounter in open water rather than near the beach where they are breaking.  The kayak I was in is shorter (11') so that might have helped with the valley. 
I also have a small aluminum boat and I would still rather nose into those wakes as I've taken some over the transom and that fills the boat with water a lot faster... that is a recipe for getting swamped.  You may take some spray over the bow, but that beats submersion of the transom and potentially choking out your outboard.

Curious to hear others opinions/experiences.

I put my kayak parallel to larger swells/waves and prepare to brace into it. 
Usually I just go up and over like a log would with no issue.

Same here, I just sit there and keep fishing.  The kayak is actually really good at handling that situation, way better than your metal boat.

Thanks for the replies. For additional context, I would say that the spacing between the waves was probably not even the length of the boat, which is why I was so nervous. With the waves so tall they were breaking that far from shore, it seemed pretty serious to me.

Interesting that you guys go parallel. I was always taught to go into the waves at an angle (maybe mainly advice for power boats?). If the waves are breaking and so narrow on top, are you not worried about rolling?

The kayak is narrow like a log and even it it breaks and fills the top side of the yak with water it will drain out.  Bracing into it will allow the kayak to slide down the face if need be. 

A boat is a completely different issue.  Open bow, low transom and wide, are not a good combinations to have when dealing with close waves like that.

I'm a whitewater kayaker, and whitewater kayakers routinely go through series of large, steep, closely-spaced breaking waves.  Here are my suggestions for dealing with large waves like the wake which you encountered when in a kayak:

1.  If you're in a pedal kayak, if you're in a paddle kayak but aren't a whitewater kayaker or aren't used to bracing into big waves, or if you're in a sit-on-top kayak without thigh straps, you'll probably be more comfortable taking the waves head on while paddling straight into them, as if you were paddling out through surf.  Even if you don't know how to brace with your paddle, each time you take a paddle stroke you will in effect be momentarily bracing on the side of that paddle stroke.

2.  If you're in a paddle kayak and have experience with whitewater kayaking and/or bracing into big waves, you can take the waves broadside while bracing into the face of the wave or into the pile of a breaking wave.  Here's how to do it: keep your elbows near your sides and your paddle by your ribcage.  As the wave hits you, stick the power face of your paddle on the face of the wave or jam it into the pile of the wave and lean towards the wave and put your weight onto your paddle.  This is a brace.  You'll pop easily over the top of a green wave, and will power through a breaking wave.  If a breaking wave is big enough, it may catch you and push you along for a ways; keep bracing and keep your weight on the buttock which is on the side of the wave until you pop over the top of the pile.  Whitewater kayakers often run big crashing wave trains sideways for fun.  When bracing into a wave, even a very big wave, keep your paddle shaft low, almost in your lap.  If you raise your hands and paddle over your head, you put your shoulders in a weak position and risk damaging or dislocating a shoulder.  When your elbows are against your sides, your shoulders are in a very strong position. 

In a whitewater kayak or a sit-inside sea kayak, you control the kayak with your lower body, in particular with your hips and thighs while bracing your hips against your back band while pushing with your feet on the foot braces.  A sit-inside kayak should fit your lower body like your ski boots fit your feet.  In a sit-on-top kayak, you have less control over the kayak unless you have thigh straps.

Here's a link to a video which shows whitewater kayakers doing a lot of bracing: