There's nothing wrong with the fuel filters if it pulled UP the hill.

The valves are OK if the motor starts easily when cold.

It's loud and horrible at idle when hot for a reason that's either an
easy fix or a more difficult one.

The easy one first. Five cylinder motors are inherently unbalanced and
shake some at idle. The problem is that its small scale shaking is an
oscillation that affects the fuel rack inside the injection pump which
controls the engine's speed. So then, the idle speed rapidly increases
and decreases and the whole car shakes in sympathy.
This occurs mostly after freeway driving that has really heated the motor.

There's a fix that's easy to do. Look at the aft end of the injection
pump - near the pipes to the oil cooler. On the pump is a bolt with a
lock nut. That's the "rack damper pin or bolt" a spring loaded pin that
ought to just bear onto the fuel rack to prevent it from oscillating.
The adjustment is to loosen the lock nut and slightly tighten the bolt
and snug up the lock nut. Too much IN will cause the motor to stall so
do this in stages of say 1/4 turn - try it - 1/4 turn if needed etc.
M-B sells a 2nd version of the bolt with a stiffer spring for about $25.
First try adjusting to original one. I've adjusted this an seen the
motor go from heavy shaking to quite smooth with a very small turn of
this bolt. Given your description and lack of prior problem I suspect
this is the motor's issue.

If the rack damper adjustment / replacement fails to cure it then you
have to consider the motor mounts - don't mix them there's a left and a
right to them.

First thing I'd do would be to run two cans of Diesel Purge through
it.