firstly, clean it up and get accuracy...you have to find your own way how to do it.
when you do that. and when you don't have messing up problems, hitting wrong notes, try to not look on every group of triplet, because you'll never get speed.
think about whole bar as one unit. or even more, 2 bars! also, focus on first note in triplet, other two will come naturally. you can practise with accent on first note in triplet. when you'll play it faster, accent won't be so strong, but will help you to control and make more clear.
for speed, all your motions should be small and economic, all big movements make you slower. be close to keyboard with your hands, not raise them much in the air

when i played this sonata, triplets also bothered me. my teacher was suggesting different hand motions, but at the end, i had to find my own. that depends on your hand constitution, size of hand, etc...
another problem which slows you down can be left hand. naturally, left hand is weaker then right hand, so try to practise left hand alone, to get same motions as right hand.
otherwise, you can get yourself at unpleasant situation where your hand won't be togehter when played in right tempo.
yes, trio is demanding beast indeed, just as rest of this sonata.

i tried to explain you but my clumsy english is limiting me , hope you'll understand what i wanted to say
wish you good luck!