3D devilry, DIY edition

Question

This is a diagramless three-dimensional cryptic crossword. Solve the clues and then fit the answers into a three-dimensional grid.

The numbering of the clues starts from the #1 (nearest) layer. On each layer the numbers go from the topmost row down, and within rows they start in the leftmost cell going right. See here for a 3×3×3 example of how a cube might be numbered.

The clues are a mix of printer's devilry and normal cryptic clues.

Across
7. Debate dropping opening speech leading to athletics event (6)
9. Books written by Roald N. Fleming and others (6)
12. Man extremely interested in Rome, looking back to make historical account (6)
15. The enemy made us disown troops (6)
17. The tribe stole carvings are extremely impressive (5)
18. Essentially agreed; you're consumed by excessive desire (6)
22. Abel's brother goes around Orange County, escaping first snow (7)
23. Number one regent beaten up (7)
24. The commander told thee: "Group at the rallying point" (6)

Down
6. Penetrating section of the Quran, covering a place with Muslim majority (7)
7. Prize lifted to storage box (6)
8. The priest read a pea's term on day (6)
13. Influence female performer (6)
14. Funny guy has odd look under constant praise (6)
16. His music will be reed (6)
19. Bad poet acquires fashionable device, starting to become sharp (7)
20. It was alto see how they would react (6)
21. There was nothing to do on Friday, so we got to start the weekly (6)

Away
1. Fall of a regularly hurtful, heartless man (6)
2. In France, the pain is persisting (7)
3. Inside canyon, end of the line for British king (6)
4. Foreign troop's Marc on Ian's oil (6)
5. A fish in each petition (6)
7. Legendary creature to wear piece of old cloth inside (6)
8. Polynesia native follows a moa, needing sample (6)
10. Do not both, erasing giant (6)
11. The G over Y level is the same: rescue the princess (5)

Answer 1

The solved grid:

The assembly process:

The lengths of the answers never exceed 7, so it's reasonable to assume that the grid will be a 7x7x7 cube. The second layer is the starting point: it must include square 10 (since the lowest 10 can be is the second layer, using the enumeration of 10-Away) and square 6 (because of 6-Down, it must be in the top row of whatever layer it's in; there's not enough room on a single layer to fit six squares into one row without creating an early Across entry, which doesn't fit).
So squares 6-10 must be placed in layer 2. DAHLIA can only intersect with DRAWER in one way, and then SALMON and SUMATRA can be placed. After that, the "core" of the grid (a 5x5x5 cube with alternating lines used for words) can be filled, and then the remaining deductions are fairly straightforward.