So it looks like your total oil income here is two pumpjacks, one at 2.5/s and one at 2.9/s. 16k / 5.5 is ~2900 seconds, or 50 minutes. It sounds like pipelayer is correctly transferring all the oil you actually have access to. Note that the fact that the underground pipes are full means nothing. Those pipes are only to show you what fluid they are carrying. From the mod description:
The pipes in the editor view are not active entities, move no fluid, and consume no UPS. They only show the fluid handled by each network for convenience. Instead, fluids are periodically moved directly from input connectors to output connectors on the same network by script.
As a result, the length of the underground pipes is also completely unimportant.
With the default transfer threshold of 2500 and an income of ~390 oil/minute (as shown in the production summary graphs), there will only be enough oil available for Pipelayer to consider it worthwhile to do a transfer every ~6.4 minutes. I don't currently see anything wrong with the mod, it just looks like you don't have enough oil income hooked up.
Your LTN connected oil supply is not working because the request threshold is set to >= 25000, but the tank only holds 24999. When I changed this threshold, a train was immediately dispatched. In the map that you've uploaded the LTN oil unloading station isn't connected to anything anyway.