I shared an idea here half a year ago. I put together a good website now, plus script, and tools to analyze the idea: https://meshnet.grok.me. By simplifying the network topology to a full mesh banking network, and then customers as spokes on banks, you get rid of chained timeouts and path-finding. Staggered deposits - which scale poorly (exponentially) as 2^N-1 but when used for only two hops they work, replace the chained timeouts. A timeout remains on last hop - there it is harmless for the “risk pay out without pay in” issue, on timeout payment simply never starts (with staggered deposit there instead, they would reach 7N, timeout better since on last hop timeout is not that problematic).
On https://meshnet.grok.me/scale, you can see optimal numbers of routers relative to payment channel size for customers and inter-bank. It tends to be very high number of routers, more than might be intuitive. Thousands. Tens of thousands. Very decentralized. With 5K per customer and 100K per inter-bank, 22K routers. 22K regional banks, each autonomous and trustlessly doing transactions with other banks to their customers, with trustless transactions with its customers. This means more speed. 22K regional banks with at least thousands of TPS between them, is millions of TPS and more.
The timeout length, boils down a bit to trust (or, proven tendency to not exploit it by refusing to release preimage, thus locking 3N deposit at your banks inter-bank channel for timeout duration). So without trust, shorter timeout. With some trust, longer.