After three days of Dominion fights and not one drop of any seal
Here's your problem. You're trying to get seals from dominion ops. First, as far as I've been able to see, you can only get one per game day (though it's not 100% when the day rolls over, i've never ever seen more than one in a day) Second, there's only a 1/20 chance it's going to be for your job.

Seals from dominion ops are just a little perk. They give GOBS of EXP, that's the real reason to do them.

If you want seals, do quests or kill NMs. There are few NMs you can't kill with 3 people or less.