Hi.
Get a microfiber towel, non-linting (like a waffle towel), fold it in 4.
Place it over the soft fabric top, gently press it, move the towel to the following section, and follow 'pressing it gentle' until whole top is almost 'dry'. Turn towel sides often, and squeeze when needed.
After doing this, it may be completely dry much faster.
Hope that helps,
Kind Regards.