talon8 is absolutely right: the best way to go about this is to use a thermometer. However, it is still an interesting question how the expected cooking time varies with the weight of a roast.
It is such an interesting question that in 1961, SIAM Review published a scholarly article entitled "On Cooking a Roast". To be a bit more precise, the question that the authors answer is this: Suppose we have two roasts with exactly the same combination of identical tissues, and the same shape except that the one is a scaled (blown up) version of the other. Let's weigh both roasts and compute the ratio between the two weights; let's call that ratio r. Suppose furthermore that the roasts have the same starting temperature, and we will cook both until they have both reached some given (higher) temperature at their centre. What can we say about the times that both roasts need to cook for?
The answer is that under these assumptions, the bigger roast will need r^(2/3) times as long as the smaller one.
So, assuming each small roast (700 and 950 grams) has the same shape as the big one that the recipe writers used (let's say 1750 grams), for the 950 gram roast you'd expect to use (950 / 1750)^(2/3) = 0.665 or about two-thirds of the cooking time, and for the 700 gram one you'd expect to use (700 / 1750)^(2/3) = 0.543 or just over half of the cooking time. In particular, for the 950 gram roast, you should expect to roast it at 200C for 20 minutes, then turn down to 180 and roast for around 0.665 * 1750 / 450 * 12.5 = 32 minutes more. (1750 / 450 * 12.5 = 49 minutes is the average time they would recommend for the 1750 gram roast, and we're using that as the base for comparing our 950 gram roast against.) Then check with your thermometer!
Finally, I think for the resting time, you might as well use the original 30 minutes, because that's not (only) about getting the internal temperature to a certain level (although it does contribute to that - the heat will spread out through the meat), but also about things like the muscle fibers relaxing and the like, which are not covered by the article.
Generically speaking meat that is appropriate for a braise is tougher and has connective tissue that can be turned to gelatin by the long slow cooking process. As you've noted, meat that is tender can be "cooked to death" using that same method, so I would, generally, recommend against using a braise.
However, a stove top braise can go quickly without ruining the meat, if you keep it short and treat the braising liquid as more of a sauce than anything else. I would suggest that you brown each side of your lamb chops, then add all your other ingredients. Depending on the amount of liquid your original recipe calls for, you might want to cut back. I wouldn't want more than 1/2 cup or so of liquid. "Braise" covered on the top of the stove for 1/2 hour, never going past a simmer. Pull out the chops and cover, while you reduce the braising liquid to make it more sauce-like, then spoon onto the chops.
Note that you won't have the long time to meld flavors, and if there are big chunks of garlic or onions, they won't be a sweet as in the longer braise. But you should get a serviceable dish.
Best Answer
This answer may be too late for you, but in general a braise can be done at a lower temperature as long as the food doesn't stay in the "danger zone" for too long. See this answer for more information on the danger zone.
For example, this recipe advise to have the oven at 300 F for an and hour per pound. In the tips section, it states that the author sometimes drops the temp to 250 F.
Braising is fairly forgiving and is typically a method used on tougher cuts of meat, so going slightly longer shouldn't be a problem.