Wow haven't been here for a long time ... but here goes.
The reason your pedal sticks down only when the engine runs is because the servo gives you more travel on the linkage and you reach the sticky point - because the servo assistance helped you reach this magic point.
Please do not take out and replace the servo because i doubt that's your problem and don't take the whole linkage out just to check.........YET
Faulty servos don't stick.
Now i cant be 100% positive without looking at your car but usually (have had a few Beta's with your problem) the bell-crank behind the servo sticks - how do you reach this?
Well, drop the plastic cover under the dashboard from the passenger side foot well.
If you look closely you will see a black blow moulded plastic sound proof cover which is trapped under a 13mm bolt securing the dashboard onto it.
You have two choices here release the dashboard completely so you can remove the item intact or butcher it (just slit it with a knife so you can slide it off (i would because you can just stick it back together after and no one will know)
Once you have this item removed you will see the bell-crank case attached to the firewall/bulkhead - there should be a locking nut and bolt running vertically through it.
The four nuts and washers around it secure the servo to the bulkhead by the way.
Remove the Philips screws that hold the black painted access cover to this box so that you can have a look inside.
You can undo the bolt now a turn or two and lubricate the crank with oil until it loosens up and fingers crossed that should do the trick.
Please try this first before you go any further "pig of a job" is correct with an engine and dashboard in the way.
You bought the silver HPE VX in Taunton ? - i spoke with the seller and he thought it was the master cylinder, of course being a sly git trying to get the car a little cheaper for a friend i did not mention the possible cause
Anyway too late you got there before me!
Good luck.