and the mutual closing transaction looked a lot like the screenshot posted above. well i paid not that much, but it also stated "overpaid by 20x". i need to figure out how to get the "starting fee" the other node will propose as soon as the two nodes enter the "negotiation phase".
Remember with lighting the case is very different to a "normal" user.
With lighting you can be in a situation where you MUST get your transaction confirmed in a block within a certain number of blocks or the other side of the channel "could" steel all you coins.
So the downside of underestimating is not just the inconvenience of having to wait - but could be loss of all the funds in the channel.
In this situation saving a few sat may not be worth the risk.