Does anyone have ideas on how to mate a flex PCB with a screw terminal block?

Some background:

At my workplace, we're using the following Keysight DAQM900A Datalogger MUX cards:

In the past we've placed the flying leads of our cables into each slot directly. However, because this requires some labor time, there's been a push to modify the cards. Specifically, we want some circuit designed that can easily be placed inside the MUX card to interface with the screw terminal blocks instead of using flying leads; on the other end, we want to add a connector with a standard pinout so we can easily purchase cables from assembly houses.

What I've done:

So far, I've decided to remove the strain relief slots, drill mounting holes at the entry for a D-Sub PCB connector (for strain relief), and run flex ribbons from the PCB to all 4 screw terminal blocks (see image with basic idea drawn for 2 of the 4 terminals):  

However, I can't seem to find any connectors that work between flex ribbons and screw terminals. Originally, I considered using FPC connectors with vertical leads: if done right, the leads could mate with the screw terminals. However, I can't seem to find anything with the right pitch for these terminals. Most FPCs have a 1mm pitch, but I'm looking for something with ~3.25 mm pitch and 5mm lead length.

Does anyone have any other connector suggestions? Or even a suggestion on a different way of going about this?

Thanks in advance for the help!

Noah

Does anyone have ideas on how to mate a flex PCB with a screw terminal block?

Some background:

At my workplace, we're using the following Keysight DAQM900A Datalogger MUX cards: 

In the past we've placed the flying leads of our cables into each slot directly. However, because this requires some labor time, there's been a push to modify the cards. Specifically, we want some circuit designed that can easily be placed inside the MUX card to interface with the screw terminal blocks instead of using flying leads; on the other end, we want to add a connector with a standard pinout so we can easily purchase cables from assembly houses.

What I've done:

So far, I've decided to remove the strain relief slots, drill mounting holes at the entry for a D-Sub PCB connector (for strain relief), and run flex ribbons from the PCB to all 4 screw terminal blocks (see image with basic idea drawn for 2 of the 4 terminals): 

However, I can't seem to find any connectors that work between flex ribbons and screw terminals. Originally, I considered using FPC connectors with vertical leads: if done right, the leads could mate with the screw terminals. However, I can't seem to find anything with the right pitch for these terminals. Most FPCs have a 1mm pitch, but I'm looking for something with ~3.25 mm pitch and 5mm lead length.

Does anyone have any other connector suggestions? Or even a suggestion on a different way of going about this?

Thanks in advance for the help!