Well I'm glad to say after doing a visual inspection side by side of both my 870 shotguns I found the problem with the tactical mode. Can you see the issue?
Here is what a good chamber should look like... (my field model)
Here is what a bad chamber looks like... (tactical model)
Notice the notch on the rail... That's what the rim of the shell has been catching, and causing the jam... Nothing a little sanding and polishing can't fix...
Edit: After about 20mins of polishing, and getting that ridge out of the rail...
I can't now pump the action, and nothing jams. Will shoot it tomorrow, and let you know how I did.
"Amateurs train until they get it right... Professionals train until they get it wrong"