Some things do sit within Congress such as the Senate adopting the insane role allowing filibuster. However, this is also encouraged by the fact the Senate can kill legislation like this. Filibusters rarely happen in the UK Parliament because the majority party can force through legislation they feel is important enough.
You say that deadlock is built in as though this is desirable. However the public just became so frustrated by the system that they just elected a madman to smash it to pieces.
Encouraging compromise and working across the aisle is an excellent property in the US system. But that has broken down and I think part of the reason is there’s no mechanism to break the deadlock that can force parties back to the table.
The US political system is completely broken with regards to lobbying and campaign finance. All the money floating around makes it nearly impossible for representatives to work across the aisle, or to ignore the aisle and vote for what their own state wants regardless of party.
If there is ever a conflict between legislative and executive, then the legislative branch can remove the executive branch.
In other words: the president shouldn't be head of government (only head of state, sort of a figurehead).
What additional authority doss the US legislative branch need? They have pretty wide authority to create any laws that don't violate our constitutional rights, I don't know how we could really expand that further (but my view is definitely biased since I grew up here).
I think congress would be well within its rights to change their own rules to add time limits on legislation or required expiration on proposed bills, for example.