I know other may not agree with this but I do think Heavy Armor Master needs a small buff for the next edition and I think you can do it early.  

1) let you take it more time with it stacking.  Ie 3,6,9 ect.  This would eat feats and it does not look like it is a 1st level feat at the moment but if someone realy want this they can get a good DR at a high feat cost.

2) Instead of making this a set 3 set it to your proficiency bonus.  This would set it to as low as a 2 at early level and max of 6 at later level.  If damage is much higher in the new edition you can even change it to 2x proficiency bonus.

That do you all think.

This is the wrong forum for homebrewing a PHB feat to correspond with UA feats, but HAM absolutely would need to be changed to be a level 1 feat fitting the Character Origins UA, because level 1 feats in there are never "half feats" - that is, they never boost an ability score, and this appears very intentional.  The probably lowest-hanging fruit there would be to remove the Str half from HAM and the Str half from Heavily Armored, leaving the other two halves: Proficiency with Heavy Armor, and DR 3 against P/S/B from nonmagical attacks.

Any further update would require knowledge the UA does not provide: to what extent does WOTC intent to embrace the changes in MPMM to how magic weapons work?  Very nearly 100% of them in MPMM deal force damage rather than magical P/S/B.  If magical P/S/B is intended to no longer exist in the new edition, you would want to update HAM to simply apply to all P/S/B, trusting magic weapons to deal force instead to bypass the DR.

Your question about scaling has very little to do with the UA's new edition mechanics (other than your first suggestion matching the UA's definition of repeatable), but if you want HAM to have better scaling, I recommend having it scale with the user's Strength bonus.

I would set it as a 4th level feat, and have the damage reduction work even against magical attacks. That should more than adjust it into being actually relevant as a feat.

I personally like tying the damage reduction to Proficiency bonus. In general I've liked most stuff that shifts focus to PB, since it's a nice reliable scale that you can hang just about any feature on and reliably know that it will grow with the player.

Quote from TransmorpherDDS >>

I personally like tying the damage reduction to Proficiency bonus. In general I've liked most stuff that shifts focus to PB, since it's a nice reliable scale that you can hang just about any feature on and reliably know that it will grow with the player.

 
Yeah, but at levels where the shift to PB would actually be relevant, how often do PCs have to worry about damage from nonmagical sources? Infrequently at most. The feat would still need to shift to also protect the PC from magical sources of B/P/S damage, and then having it tied to PB might be too much. What do you think?

I agree. Just limiting it to bps damage already limits it enough... Excluding magical damage feels like it was almost deliberately designed to make the feat useless. If I was DM I would just ignore that limitation anyway