How do movements while concealed affect alien patrols?

Solution 1:

The observation, that enemy pods have a tendency to converge on your squad, even if you remain concealed is correct.

once I neared the objective, all three pods on the map converged on it, leaving me no options but to evac or to fight the entire enemy force simultaneously. Clearly this convergence is real, and some mechanic must drive it.

Judging mainly from this post, there are two gameplay mechanics coming into play here:

Line of Play

• LOP uses a line that is vitrually drawn between your squads average position and the objective to potentially move enemy pods into your way.

UpThrottling

• If active, steers the closest enemy POD towards the current line of play.
• Kicks in after 2 turns (default) without enemy contact. Is defined in the XComAI.ini.

Essentially, after two turns of no contact, the AI cheats and sends the nearest pod to move to a location between you and the Objective.

There is another thing that most people encounter sooner or later: Pods suddenly stop moving when you come into their sight range, even though you are concealed. This often causes a "dead-lock", where you are no longer able to move without activating the POD.

The picture below shows the actual LOP drawn in debug mode. Notice how the start point is located at the weighted center of the squads position.

There is also a reference to the patrol behavior in the Long War 2 Wiki.

In vanilla, there would always be one pod that would be stationed between XCOM and the objective. If that pod was killed, another pod would move to come between XCOM and the objective. Even if the pods were not active, they would, in a way, know where XCOM was. In similar fashion, pod patrol routes would dynamically adjust based on the location of XCOM.

This behavior was completely changed in LW2.

There is also a workshop mod that attempts to remove the LOP/UpThrottling, but from own experience and judging from the comments there seem to be some issues.

Regarding your claims/assumptions:

1. Enemies can hear you when you dash, and will move to investigate the noise.

I do not think this is true. I did not find any conclusive information, that any form of movement (except when breaking windows for example) is causing noise. Regardless of distance to the enemies.

2. The mechanic is specifically triggered when you're close to the objective; if you get too close to the objective, the enemy sends a patrol there.

Distance from the objective does not seem to be a criteria. Its just Upthrottling kicking in.