Maybe you could consider using Auto Placement (Place > Autoplace) to place the components based on the auto-placement grid.
Here are the quick steps:
1) Setup > Areas > Package Keepin - Define shape where components can be placed, required by the next step.
2) Place > Top Grids - Enter the X and Y Grid increment and indicate the origin point of the grid lines.
(This will add a hatch grid on Board Geometry / Place_Grid_Top used when auto placing components)
3) Edit > Property - Add the PLACE_TAG component property to all the parts you wish to auto place, could select them all.
4) Place > Autoplace > Design - This will place all the components with the PLACE_TAG property within the board outline on the placement grid defined in Step 2.
(Note: Use Place > Autoplace > Parameters to change the component origin point; Body center, Symbol Origin or Pin 1)
That's it. Play with it a little bit. Sort of a weird use of the functionality but it may give you what you need.
The one major difference compared to Quick Place is Auto Place places the components on the board using the hatch grid defined on Board Geometry / Place_Grid_Top and Place Grid_Bottom subclasses.
Hope this helps,