Firstly, I don't envy you! I completely understand about not being able to afford another seat, though. We took our son, then 22 months, home to Ireland for Christmas one year and it was a 10-hour flight and we were pretty nervous. I don't know how it happened, but even with a full flight we somehow ended up with a seat between us! It was heaven and he slept all night, no sleep aides required (not a sleeper, so I was looking for drugs to help him out, too, though also not a big fan of drugging!). But what you can do is ask for the bulk head seat or the seats just behind first class. We had those seats coming home and it was a god-send. I put a blanket over my legs, rested my feet on the wall and called it a fort and my extremely rambunctious and incredibly social son played under my legs for two hours by himself!!
A few things I would recommend. Firstly, we flew American Airlines home (I will never fly with them again) and one of their stewards was soooo rude to us and kept asking if our son was really under 2 (like they don't check everywhere!). When I asked him if he would like to see his passport, he declined and walked away. Anyway, he refused to give our son any of the airline meals (on an 8-hour flight!!!). Since we had gotten to the Dublin airport extremely early, there wasn't much open, let alone there for our son to eat so I just assumed he would eat on the airlines. Disaster. I was told only customers with seats get meals and that we would have to give him some of ours. They are small enough anyway, and I was 10 weeks pregnant with twins at the time and so incredibly hungry. We waited until the end of the meal serving and did end up getting an extra one, but seriously, he was not going to feed our son otherwise!! That said, make sure you bring a looot of food he likes (bagels and cream cheese? Sandwiches? Yogurt? Fruit? Even chips or raisins or whatever - you can buy all of this in the airport in Seattle, but I've never been to the airport in Portland). Just carry everything that he likes and extra! The airline security (even the crappy ones in Seattle) are usually pretty good about letting us through with even full bottles for our babies, etc. Also buy water or other drinks as it can take forever for the cart to come through...
Pack at least two changes of clothes and lots of extra diapers and even a shirt change for you and your husband (no sippy cups or lids on the airlines and close quarters so drinks can fly in your face pretty quickly!) If you have one, bring a portable DVD player, especially if you have a long layover or long wait in the airport (I'm assuming he'll watch cartoons, but maybe not...). Bring kid-friendly earphones (a lot of flights are switching to earbuds and they're too big for the kids ears!). If you're lucky, you'll get a flight with the individual screens, but it's always good to have a portable DVD player as a backup! Bring lots of toys to distract him with. I usually buy a few new toys for flying so that the novelty lasts longer.
Also, you might want to bring a favourite blanket or toy for nighttime and don't forget a couple of books to read to him when he's really bored and tired and cranky and needs winding down. A lot, I know, but what you can stuff into your bag can really make a difference! That said, I would use backpacks as carry-ons as this will leave your hands free. I usually travel with a small child-carrier, too as this can be very hand for getting on and off the plane (we have three small children, though, so with one you might be fine).
Some airports have family lines for going through security, so ask about those.
That's all I can think of for now! Have a great trip! For the record, I would totally do it - don't listen to your pediatrician (he/she may just not like travelling!).
Oh, and another snack idea - cereal bars. Very handy! You can get the softer ones like the nutribars, I think they're call... or whatever.