Gap between perimeter and infill

I presume much of this is due to resilience of the belts and motors where there is a small amount of hysteresis. The head doesn't quite reach the intended position.

Some articles make this a hardware cause and offer no solution; where the obvious solution would be for Slic3r to overshoot the infill turnaround point slighly so as to encroach onto the perimeter in a controlled way.

Does Slic3r have this option/capability?

There's a setting in slic3r to set the overlap between the infill and the perimeters. That said, maybe your nozzle is too high above the bed for the first layer and the plastic isn't getting squished down enough for the lines to overlap. Or maybe your extruder calibration is off and it's under extruding. Or both. Or all three...

Belt drives in 3D printers should not have any backlash. If you have backlash in the mechanism it needs to be fixed. It will cause other problems, too.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]