By pruning back the top you will encourage the side shoots to break further down.
I wouldn't feed at this time of the year as it will only encourage new soft growth that will be susceptible to frost in the winter
You could give it a mulch to overwinter with and a balanced feed in the spring
Then if you get long sideshoots in the spring and not much else cut them back as if you are pruning them, all of this will encourage a thicker, tighter hedge

they take quite drastic pruning. a neglected 60ft [yes 60ft] beech hedge was pruned down to 20ft then 12ft the year after. we didn't feed it just kept it well watered. It is back up to 15ft now and needs another prune.

We find pruning the height within reason down isn't a problem but if you want to take it down to 4foot 6 I'd perhaps not do it all at once as it involves sawing through thick branches. It will want to be quite wide - after all it really intended to be a row of huge trees. I'd cut it all neatly as normal this early autumn and then try cutting one of two plants to the height you want at the end of the hedge that doesn't show. See what happens and if it regenerates well you can go ahead with confidence and do the rest.
SBG you were very brave - must have been quite a task!

brave or foolhardy but OH was determined to get some light into the very very shady garden. broke a few fence panels in the process though :o)

Well worth it though!