...this is what I would do.
The goal here would be compatibility with the original but any IP would have to be avoided.
*Replace the rulebook combat mechanics with the ones from the Battle Manual (in particular the improved blast weapon, overwatch and sustained fire/following fire rules)
*A Choosing a Target system that's a bit more structured than "each of my 30 guys can shoot at anything I like" but not as chunky as the Battle Manual/2nd edition system.
*Replace the Reserve phase with the 2nd edition Run move.
*Replace the Rout and Psychology rules with the 2nd edition versions.
*Keep the psychic rules but rewrite pretty much all the actual powers to be more interesting and more applicable to the table.
*New weapon lists would take a little bit of a page from 8th edition in using lower save modifiers and damage values in general.
*Weapon lists by era (low tech, high tech, futuristic) for multiple settings.
*Use the vehicle rules from the Compendium/White Dwarf (with the various damage tables). Maybe ?
*Create a list of Traits (similar to the Universal Special Rules in newer editions)
*Create new troop types to include in the book, mainly inspired by video games and television.
Klingons vs Daleks ?
(Also, I just realized the spell check accepts both Klingon and Dalek without complaint)
*Sort out a really cool mission system for randomly generated scenarios that would require troops to do more than just shoot each other in the face.
* * * * *
NOW......If I was doing an "advanced" version, I would do the following as well:
*Do away with Initiative and Attacks on the profile.
Instead, Weapon Skill of 5-6 gives you 2 Attacks and 7+ gives you 3.
*Consider getting rid of Strength as well.
*Use the Space marine morale rule (shaken on first failure, broken on second) for all troops.
I would also be really tempted to "flip" Ballistic Skill, so you are rolling equal or under your BS, instead of the whole "7 minus BS is your hit number".
That way you could just apply hit modifiers directly to your BS.
But rolling under instead of over might be a "bridge too far" for the old timers?