First of all, I appreciate the simplification done by this mod in removing the need to specify a provide threshold.

I am aware of the part of documentation stating that a custom provide threshold can be implemented with a decider combinator. However, I have no idea how to override the provide threshold with a lower threshold. Or in other words, how do I trigger a train to pickup from a station with insufficient items to fulfill the requesters, without modifying the requesters' request threshold?

It is not a common use case but in my setup I will sometimes require a lowered provide threshold to:
1. Decommission stations where I need to force items out regardless of request thresholds
2. Implement clean-up station, same reason as above
Both of which I wish to achieve without the need to alter the requesters' threshold - so that the items can flow according to the requesters' scheme.

Currently the only way to do this is to trick the station into thinking it has the items. I'm not quite sure of an elegant way to allow users to specify that. Perhaps I'll make the input of the station info combinator allow you to override the request threshold for a provide stations. I am worried however this might be unintuitive to people creating provide-request combo stations.

I don't mind tricking the station but how do I kick a train out with the cargo condition?

manually sending it unfortunately

Now in version 1.2.0 the input of the station control combinator allow you to override the request threshold for a provide stations. This allows you to easily implement your ideas for clean-up and decommissioned stations.

Thanks, just to clarify: provide threshold only applies when the station is in "Provide only" I assume? So I can do both station "request" (provide) threshold and item-specific thresholds using the station control?

No they always apply, so you have to be a bit careful using this feature with combined provider and requester stations. As usual if you just stop a combined provider and requester station from receiving a positive signal for items being requested there will be no issue. You have to do that anyways with combined stations.