I'm running a 5e Planescape campaign as we speak. A few things I did:
- I dropped the whole magic weapons +/- by Plane table. But to emulate the "geographic magic" theme, magic weapons may gain their numerical bonus depending on the plane the characters are on. For instance, at low levels, they found a magic sword that functions as a magic sword for the purposes of bad guy resistances (i.e. does full damage), but it was forged on the plane of Ysgard, so it only gets the +1 when used on that plane. Later, they found more powerful items that broadened their usefulness - a "holy" sword that received its +1 on all good-aligned planes, for example. Or an elemental air sword that get's an extra +1 against earth creatures. Just baking a conditional bonus into the magic item description keeps the feel without the fiddly table.
- Using Quickleaf's stuff as inspiration, but simplified, I instead treated the Factions like an additional background. When you choose your faction, you gain an appropriate an additional proficiency (hasn't broken anything yet), plus some bonus perks (different based on the faction, of course, and largely pulled/modified from the Factol's Manifesto). For instance, Ciphers can add half their proficiency to Initiative rolls, Godsmen add half prof to Persuasion rolls, Sensates get Darkvision and extra gold and a few other things, etc.
- I tied Faction Inspiration points to a renown system, like in the DMG or AL - you can earn renown points by doing things for your faction to gain you notice. After earning 3 renown points, you can start earning Faction Inspiration d20s for acting on your beliefs, which again varies by faction (much like regular inspiration is gained by acting on your bonds/flaws/ideals). Ciphers can use their d20 to re-roll initiative, Godsmen can re-roll social interaction checks, Sensates can re-roll Insight/Perc checks, etc. As they gain further renown points, they may eventually gain ranks in their faction with additional abilities. Some of my players have really got into this, others not as much, and that's totally fine. I want to encourage the concept of "beliefs change reality" without hammering them over the head with mechanics.
- I actually kept the flavor of the spell alterations by plane, for flavor. The mechanics might need tweaking a bit, but the general ideas are the same. If something gets cast at a level lower or higher, just take away or add a damage die. In the case where effects get changed, just play it by ear. Most of it is fairly transferrable though - for example, where water spells don't work on the Plane of Fire in 2e, they don't work there in 5e either.
- Oh, I also created some custom backgrounds, based on the kits in the Planeswalkers Handbook. My guys could take Chant-Broker, Spiv, etc., which were generally just variations on the backgrounds in the PHB (which were also open for use).
Otherwise, it's all fairly straightforward conversions from 2e mechanics to 5e mechanics. Just look up the equivalent trap or monster in the 5e MM and use it, 5e is fairly forgiving about that. All the fluff and window dressing is exactly the same.
Hope that helps, I'd be happy to share more specifics on my faction stuff if you're interested!