I don't hunt deer, but I do go after hogs. Some of the larger hogs (250 Lbs or so) are probably tougher than deer. I just use Hornady Interlocks, either 150 or 180 grain. The 150 grain bullets will go right through a 150# hog. The 180's typically pass through anything I can find to shoot. I've recovered a couple of the 150 grain SP bullets, they expand nicely and I have seen no reason to try anything more expensive.

Do the still make 200 gr. interlock for 338 cal.

Yep, you can buy the bullets for reloading or their ammo in the Superformance line of products.

Hornady will tell you to keep the COAL the same. I couldn't get the GMX's (30/06, 300WSM) to group very well. Once I widened the jump gap, I got the accuracy I was looking for.

A 7mm-08 duplicate the 7x57 Mauser and with their modest velocities has always worked well with traditional cup-and-core bullets. Any good 140-160 grain bullet will exit on a whitetail at 150 yds. The super-bullets of the last 25 years are designed to cope with the disintegration of conventional bullets at short ranges at high (>3000FPS) impact velocities. Not a problem for you.

GMX are great bullets and I use them myself when loading for my wife's 7mm08 for elk hunting.
They kill deer with well placed shots too. You just have to follow a longer blood trail.

No need for fancy mono metal bullets on deer, of all my rifles only my 06 is running a mono metal (TTSX) and only because it is for those places where I am just as likely to run across a large hog as a deer. Everywhere else and in all my other guns I use SGKs, Ballistic Tips, or SSTs and have been impressed with the results.