I'm really curious now - how do people play engine decks/shuffle them when they are finished with a turn? Just scoop em on up? Do you throw down the handful of victory cards prior to doing the scoop, or do you discard them and then do the scoop?
I hadn't really thought about it. When I play, I place actions in a tree structure to keep track of actions, and then treasures off to the side after I'm done with my action phase. Usually, afterwards I'll rearrange them when counting the total treasure, especially if it's a huge engine; it's easier to place them in groups and be like 'ok, these four grand markets get me one province, these four treasures get me another, and the remainder here is $X which I spend on other stuff'. Whatever green is left in my hand I just hold on to or put down. Then I pick everything up, put it in a deck and start shuffling.
Can't you manipulate the way you scoop to influence the outcome of your deck to the same extent as ordering your deck?
Yes, manipulating the scoop to influence the outcome of your shuffling is the same thing as reordering your discard to affect your shuffling which is equivalent to lots of other undetectable but unfair tricks to manipulate what happens post-shuffle.
Does any of this change if the intent is to avoid the non-random clumps as opposed to ordering the cards for a better turn?
If your intent is to avoid some particular card ordering - then that's inherently non-random!
There's nothing 'non-random' about clumps. What IS non-random is deliberately manipulating what cards go where in order to prevent them.
If you have a good shuffle, then clumps will appear as often as they're statistically likely to appear, with no need to pre-arrange the cards. If you have a bad shuffle, then a lack of clumps is just as non-random as a clump.
If you're deliberately changing the order of cards, while looking at them, before you shuffle, the ONLY reason you could possibly be doing this is if your shuffle isn't good enough and you're attempting to influence the deck order. The solution to this is to shuffle more, while not looking at the cards.