No you can't. Headspace is not the only issue here. The Ultra is beltless and fatter so no fitting problems there because it wouldn't. The 7 Rem mag would probably chamber. Lots of headspace due to body case length (gun damage, personal body injury maybe even death will occur). Your 7 STW is a 8mm Rem mag case necked down to .284 caliber. The 8mm Mag case is a 375 H&H case necked down to .323 caliber and a sharper shoulder angle added. Playing with 60- 80+ grains of high rate burning rifle powder = hospital or morgue.
Don't do it. 8mm Mag case's aren't that expensive to buy and neck down to the STW if you aren't doing so already? (Start reloading) for this rd. I own and reload for the 8mm Mag. It's as cheap as most popular magnum chamberings to reload for. The factories take advantage of unpopular chamberings such as your's and mine and therefore raise the $$$ bar because some don't bother to reload and thus are stuck with factory stuff which by the way are feasable at the most in terms of accuracy and power. Would you rather pay $70-$80 for a box of 20 rd ammo, or invest about $20 to $150 more on a good reloading kit that pays time and time again on less than half that cost on the box of ammo? And you customize it yourself to shoot what you want.