My suggestion would be, firstly, to create outlines of the shapes (if you haven’t already) and scale the whole lot way up. Working at a much bigger size gives much finer control of things like that.
Check your Snap settings. You can turn them off or adjust them to suit how you work. The other option is to use snap to guides and then use custom guides only where you need them.
You can also use the Align palette to help you out as well.