>>64408427 (OP)
Give the tube a spring, follower, and "follower handle" on the follower like an 1860 Henry or Volcanic Repeater. The tube is filled with rounds. The spring+follower blocks rounds from feeding after passing the drum's opening. When the gun is empty, simply push that follower back forward and let the drum fill the tube again (think: drum mag spraying out rounds). Gravity may have to assist getting the rounds towards the receiver (point muzzle at 45 degree angle up). When filled, again let go of the follower.
Alternatively, the follower and spring is somehow attached to the pump and the tube holds only one or two rounds. Pump has to be attached to that follower or at least have an arm interacting with it. You pump and a rack and pinion attached to an arm of the pump shoves the follower forward to pop another round into that mag tube when you close. How one keeps spring tension on the next round as you pump forwards again, I don't know. Maybe one round is always on the lifter as the bolt closes so it's pretty much self-ghost loaded at all times. I'm sure you could make it work if you had enough time.
>>64408554
My god...