Awesome concept (and we really need more heavy weapons yes PLEASE)!
I'd say the stats you chose are pretty good, but I think it could still use a bit more of a debuff.

My thought is that, given it's a 'shield' weapon, and given his stance when using it and the overall look of the minigun, that having a 5-8% (number is up to you, really) decrease in movement speed while depolyed.

Logically, think about it. Attaching an extra 40-70 pounds of hard steel to an already massivley heavy gun? He should be slower.

That is a troublesome buff, given how slow Heavy already is. So another possibility, given how slow he is, would be a small increase in spin-up time, to compensate for the decreased movement speed. Perhaps something like 5%?

This weapon would therefore become something like a Tomislav with it's potential to suprise people, except it's not practical for suprising.

What this gun would be most useful for is for Heavy to be able to get to the front lines and go into defence mode pretty fast and become the ult. tank, just sitting there and absorbing damage as his team recouperates or tries to push forward/distract the other team.

I would use this weapon, absolutley. It would be very, very fun and incredibly useful in things like MVM and defence. I would use it with the Gloves of Running Urgently, so that I could get to the front lines asap, and I'd pair it with the Sandvich, of course, so that you don't die as frequently and can really become a hardcore support character.

This Heavy would become a nasty target for Spies (moreso than normal) and Pyros, while be able to combat Demomen and Soldiers easily.

TL;DR:

+5% spin-up speed

• Want to be able to get into action very quickly.
  
• Compensation for slow movement speed.

-8% movement speed while deployed

• Very heavy weapon.
  
• Purpose is to become even more of a meat shield then you already are.