The 7mm RM pushes a bullet to pretty good speeds. Make it a light-for-caliber bullet like a 139 and its moving very fast, likely 3000-3200 fps. Take all this speed and add a traditional cup-and-core bullet like an interlock, and you can reasonably expect some over-expansion, particularly on a hard bone. It might be different if you were talking about a 139 grainer built like a Barnes TTSX. I would not use your interlock 139 bullets at full 7mmRM speeds.
However, you could slow them down some. Instead of loading to max speeds, down load them to a more modest velocity. Load them to 2700,2800 fps and they will open very reliably, with far less chance of over expansion. Penetration will be deeper. In other words, take your 7 mm Rem Mag, and load these bullets to mimic a 7mm-08. You won't be using the full capacity of the Magnum, but the bullet will behave much more reliably.
If you want to anchor him right on the spot, forget using velocity. Use shot placement. Forget the lung or heart shot. Try to take out the vitals AND the skeleton as well. Break both forelegs while shooting the heart and he won't be able to go far, and will bleed out before he can go 20 yards. Or use a high shoulder shot and the shock to the spine will drop them right there. They bleed out with the lungs gone before they can get going again.