Glad others are looking at this.
Yes, suspect most of the (4)'s combine to make real word (8)'s.
The 4x(5)'s + 4x(6)'s are the key to start populating the grid - but haven't got enough of these yet.
Have about half solved, but could do with some hints on the following:
1. Natural system that's before food or late for starters
11. Supports second-rate prince
14. See some wicker, perhaps
17. Docked wild flower in disused estate
19. Ran from immobilised African flower
37. King ousting Queen in warship returning to Scottish reach
50. Star needs energy to play
52. Pollute lead-free contrivance for stirring molten metal
57. Conjunction seen when hospital is covered by dust
59. Manipulates seconds from pairs of punsters