Clevie..that sounds right EXCEPT that there is no reef "between" Dalila and Palancar Gardens, they run into each other. I saw this thread and checked with a person "in the know" on the island because I have never heard this name and it seems I have been diving there quite a bit......hahha. I think that the regular old Palancar Gardens is long enough that most dive ops have clients who run low on air WAY before they get to the very end. But PG winds into shallower water IF you make it to the end, then there is a little sandy stretch and kaboom, a large coral head which is the BEGINNING of Dalila. Most captains, when asked for Dalila, drop much farther north and so it's easy to miss the beginning which IS quite beautiful. (we won't get into how many captains confuse Dalila with La Francesa......).
If you're interested, another "too soon" drop off IMHO is San Francisco Reef......again, it's a long reef and so the cappy's normally drop off over the part that is already shallow..........but if you actually get dropped off at the very very start, (it is deep with a sandy bottom rolling over the wall, so you MUST watch your gauge and not go TO the bottom) then there are several coral heads FULL of crazy good stuff. (I have seen numerous green morays and nurse sharks in there on a single dive......they must be laughing that the divers are dropped too soon......hahha) After a bit you are back up to the shallow part, great for your second dive, but the start is only about 60-70 feet max if you swim to that depth and the six or seven coral heads on the slope.
Glad you found your answer..........enjoy tomorrow!