if hundreds to one is what you want, have you tried the following
1 estimate/measure the gap between the polygons to get some sense on the space you need to close (ie say 10 meters)
2 buffer the polygons using the dissolve option, using a buffer width slightly larger than your estimated gap in 1 (say 5.1 meters). At this stage you should have one big polygon with no gaps.
3 negatively buffer the result in 2 ( ie -5.1 meters)
This should hopefully, but no guarantee return what you want, but this will depend upon the polygon configurations prior to the initial buffer.