Here's a primer on NATO and Zulu straps and others.
Authentic so-called NATO straps (both
G10 NATO with "keeper" and the single layer
RAF NATO styles without a keeper) are made of thin woven nylon as originally specified by the UK Ministry of Defence (MOD). There are many copies on the market. Most of them do not conform to the original MOD DefStan specifications for a nylon watch strap in 1973. The G10 type has three rings and a buckle and can be worn on the wrist with a foldover going through the third ring or over a wet suit sleeve without a foldover. The RAF type is shorter than a G10 and has two rings and a buckle. It is meant to be worn directly on the wrist and is not meant to be worn over a jacket sleeve. There should be no foldover. As both types are made of the same nylon they were designed to be trimmed to size by the wearer to their wrist circumference.
The keeper on a G10 prevents the watch head from sliding around the strap on the wearers wrist. There is also the added security of a G10 type's foldover when threaded back through third ring near the buckle.
These two types are generically called NATO straps because NATO did the original specs and MOD adopted them. The originals were stamped on the buckle NSN for NATO Stock Number. G10s have three rings; one to accommodate the keeper at the middle and two for the fold over. It was called G10 because that was the MOD requisition number. Original MOD milspec straps are grey and 20mm. Any striped ones were and are civilian. Phoenix Straps Ltd. made them originally for the MOD to DefStan 66-47 (now obsolete) and still produces them.
Waterborne Safety Strap is a copy of the G10 (with a keeper to prevent sliding the watch head from sliding on the strap) and was marketed to recreational divers. It is 11" long; same as a G10. It is made of nylon webbing, has four heavier rings and the same "double buckle system" (a Waterborne marketing term) as the G10.
Zulu is a Maratac trade name. Maratac Zulu was introduced to compete with Waterborne in the recreational dive market but does not have the keeper feature. They are 17" long to fit over wet and dry suit sleeves. A Maratac Zulu strap has two rings and a buckle. It is made of a thick ballistic nylon.
Maratac also makes other types of straps sometimes incorrectly called Zulu. Neither Maratac Zulu or Waterborne straps are milspec.
As both Zulu and Waterborne straps are much thicker than NATO types two compromises exist. One, as you discovered, is that many watch head lugs don't have sufficient clearance between watch head and springbars to fit through. The second is they are bulky at the fold over end, sometimes going over twice, and as such protrude quite a bit on the outside of the wrist inviting snagging.
Additionally are several NASA types. They are made of Velcro webbing instead of a buckle and are longer than any of the others to fit over an astronaut's pressure suit sleeve. They have no keeper and one ring.
All of these strap designs will keep a watch head on the wrist should one springbar fail. Obviously a two-piece strap of any material won't. Many milspec watch heads are spec'ed with fixed lug bars to prevent a springbar failure. Screw pins or screw bars rarely fail but yet allow two-piece strap changes.
