This thread piqued my interest, and I've been extensively twiddling with decklists. Though I haven't played any games yet (I'm busy transitioning to a new job), I'd like to share a few thoughts I have, so feel free to berate the fact that I have no play experience with NEXT since Opening Moves.
First and foremost, I really, really don't think NEXT Design decks are similar enough to ETF to make the argument that you can use them interchangeably. The lost of 1c per turn is huge, and I feel as though you want cheaper ice in NEXT anyways so that you get full use out of its ability by being able to rez your ice first turn without too great of a hit financially (so less liberal use of Tollbooth and Heimdall). Secondly, such ice (Eli, Viper, etc) lends itself to the midgame best, and less so at lategame once the runner has fully assembled a rig and economic engine. As such, forcing through 5/3's or 4/2's through a remote at the end of the game seems impractical in too many cases to warrant their use. Supposing my argument is correct, I think all would agree such a deck would be quite different from a HB glacier such as Red Coats.
I see two cards in particular that thrive in this style of HB deck moreso than in other, more popular archetypes. The first and already discussed is Mandatory Upgrades, and the second is Haas Arcology AI. ManUp is highly conditional, as you need a scoring window of 2 or 3 turns, enough economy to advance and rez ice, and adequate ice to protect it. However, if scored, it all but guarantees the Corp is able to close out the game, so a deck dedicated solely to scoring ManUp quickly may be worth looking into (I'd recommend running 2-3 ManUp and 2 Fast Track). Haas Arcology is interesting in that it's basically a win-win: the runner either spends resources getting to and trashing it (which is great for HB tax decks and can open up a scoring window), or the runner ignores it and the corp can score 1-2 agendas out of hand over the next couple turns.
I need to get around to playing!
Edit: for a dedicated ManUp build, I'd probably go with 3x Hive, 3x Caduceus for influence or something similar.