Well im thinking the blended seaweed bucket is polly doing to do a lot better then the whole seaweed one. You dont want to be dumping pieces of partially decomposed seaweed on your plants soil, thats gonna attract bugs. But I have never tried it myself so who knows, I think its great your testing both.
Since its bacteria that will be breaking down the seaweed, I think helping the culture get started could be good. I think a lot of bacteria feed on carbs, and a nice carb a lot of people add to their teas to support a bacteria culture is black strap molasses. So adding a table spoon of molasses to each bucket could help. Another idea is to use filtered or bottled water, since most tap water has chlorine and fluoride that would kill bacteria and therefor slow down the decomposition. A final idea is that you could add something containing beneficial bacteria to get the process started. I am making worm castings to get beneficial bacteria in my garden. If you get some (roughly a handful maybe?) earth worm castings and/or soil from a near by forest, put it into some pantyhoes or something (to keep them from mixing into your nutrient solution and eventually clogging your sprayers or anything like that) and put that into your bucket full of water and seaweed then the bacteria from the castings and or soil could inoculate your bucket and start breaking down the seaweed. Those are some strategies that i learned from reading about producing healthy beneficial bacteria populations in teas and I think that the same ideas could apply to what your doing.
Good luck!