Your cook plan will work but you'll need to be careful on the serving side. A London Broil is a very chewey cut and HAS TO BE sliced very thinly across the grain to be edible. I know one guy who tried to serve it like a steak and was horribly disappointed. At 140 before rest should give you "medium" with pink, warm center.
The most common way to prepare this cut is grilling on high heat, searing on both sides until medium-rare then slicing into very thin strips (often served on salads)
An alternative is a "reverse sear": Smoke the cut at low temp (160 - 180) for an hour or so to infuse some smoke flavor then move to a hot grill and sear to finish doneness desired.
London Broils have wonderful beefy flavor but can be like shoe leather if you cut with the grain or too thick.
Hub