When I'm trying to speed up carbonation of bottles, I'll place them on the wooden floor in my utility room which contains the clothes washer, dryer, hot-water heater and furnace--all in a relatively small space.
It's warmer than elsewhere in the house and the vibrations of the washer on the spin cycle and the spinning dryer drum may also help keep the yeast "roused."
Some brewers like to use a plastic bottle and squeeze it periodically to check the progress of the carbonation.
I prefer to sample it beginning on the fourth or fifth day after bottling even though I know it will need more time. At age 71, it's like Christmas morning all over again each time I get to sample a bottle of something I've brewed.
I cold crash my beer, but I don't filter it. The last few bottles from the bottling bucket usually may have a bit more sediment and air in them so I drink them first for my own consumption.