I wouldn't recommend too much gouging of torsos. Better to get flat missile plates, and put them on top of the existing torsos, filling any gaps with putty/clay/etc.
Problem is, where do you get plates with 15 missiles from, that will be small enough? IWM has a whole series of launcher plates, but the 15-hole one is on their XL Launcher Plates item, with two strikes - a) it's way too big, and b) you'd need to get two packs to get two LRM 15 launchers. Consider using the MRM-10 plate in the Medium Launcher Plates set - okay, it's not got the right number of missile holes, but either a) don't fuss it, or b) say more efficient Clan tech launches 15 missiles from 10 holes in 10 seconds.
An alternative might be MW:DA parts. The JES III has two pods, each with two LRM-15s. Slice the front off one of these pods, then divide down the middle - voila, two well sized LRM plates. There may well be generic items you can find from other suppliers which would suit, particularly if you have problems with finding one JES III at a good price.
Don't forget to remove the ERML tubes off the left arm, and fortunately the right arm is just the MPL and ERSL mounted straight at the shoulder. Maybe try scratching up a shoulder plate for the right arm?
Cheers!