-snip
Why don't you open a channel with
LNchat's node?

I reboot the server manually once a week so the downtime is negligible.
I guess it's in anticipation of the funds going out that they are "parked" elsewhere.
Coins are locked in a multi-signature address which is in control of both parties.
I'd say the funds don't go to miners, but to the "nodes" carrying the signal. I might investigate seeing if I can keep a couple of connections open.
The Lightning Network is an off-chain scaling solution so that's why miners don't participate in payments (except when closing and opening a channel). It works thanks to
Hash Time Locked Contracts.
Plus there doesn't seem to be any actual way to send my funds out, I have to wait for a funds request to come in.
That's a known problem which has been already addressed.
Sphinx solves it but it's available only to nodes which update to a specific branch.