Slice then Dice
I'm spending a few days each week working at our Manchester site. I've not been down here for a couple of years and, today, I bumped into a chap I spoke to way back in 2013. I couldn't remember his name but I remembered our chat. He is an experienced PM, he works in a waterfall environment, and we talked about if there was anything he could cherry-pick from the Agile world. There was.
I told him that, imho, the simplest thing any PM could do to improve their waterfall environment was to slice each big project into 2 or 3 or 4 smaller projects. The first project builds a base which the subsequent small projects build upon. The second small project fills in the gaps. The third and forth fill more gaps, or exploit opportunities discovered while releases 1 and 2 have been live - though, sometimes you'll decided not to do 3 or 4, and invest your money elsewhere.
Anyway, I bumped into him again, he told me his name, he said he'd done as I'd suggested and it had worked wonderfully well.