The difficulties you have mentioned, the potential for huge lambs, also fat in the pelvis can make for a difficult lambing due to lack of space. Be prepared to assist and if not coming easily, call the vet promptly.
It is very hard to scan a ewe (or other animals) close to birth, but an experienced shepherd or vet will often be able to tell if a ewe is heavy in lamb by "bumping" the belly to feel for lambs, or tell from udder development.
Feeling spine etc to check her actual body condition score is very good advice, an experienced shepherd or vet will be able to help you with this.
When did the ram come out, this will let you know the latest possible date she could lamb.