How can I move within a block?

If just walking to the right point is too fast for you, there are ways of slowing it down. Crouching, drawing a bow, walking on soulsand, getting stuck in cobweb, potion of slowness, potion of turtle master, a bunch of other less practical ones. Also, combining them all reduces speed further.

Break the blocks on the floor around you except for the one you want to stand on. Hold crouch and you won't leave the block when moving around because crouching stops you from falling into gaps. Found the perfect vantage? Leave your keyboard and use your mouse to replace the blocks.

Try a variety of block selections to use as your balance.

Okay, from the comments on your previous answer, you would prefer not to break blocks around you. If temporary destruction isn't an option, try temporary construction instead.

Instead of breaking blocks around you, place blocks around you. You can then walk up to them and fine-tune your position, then break them afterwards. Also try using other types of blocks to press up against like fence posts, and open trapdoors. This will allow different points.

(I'll be honest, I'm throwing ideas at the wall to see what sticks. Hopefully one of these method works for you.)