Basically the answer to you problem is to use the Nudge function (I can't believe I did not think of that).
I learned this by contacting the Product Designers at Graphisoft to ask them about this issue.
So the idea prior to AC15 was that after activating Grid Snap the program was most suitable to element placement. Selection, Drag/Rotate, Parameter Transfer etc. operations worked in a random manner as you could only use them in such a situation if the element was placed on the Grid. But e.g. you could not drag a point on an element to a Grid position. So there were limitations.
This was changed in AC15 so now during selection operations Element Status is stronger than Grid Snap, which then reverses during editing (Grid Snap will become stronger). So when Grid is ON the editing operation can be started from any point of an element but can only end on a Grid Point (which is your case).
With this change the usability of the Grid has increased, however it is now not usable in your situation (although it is not even recommended for that case).
So in your case when you want to move something at Grid intervals, just select the element and use SHIFT+ALT+UP/DOWN/LEFT/RIGHT key.
Please let me know how you feel about using Nudge for such cases?
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