Within the context of bounded accuracy, the level-bonuses and stat-gains in the 4e Epic tier have to be set aside. That leaves hit point gain, plus a slew of powers/features: the features from epic destinies (Level 21, 24, 26 utility power and 30) plus epic feats. (There is also the substitution of higher-level attack powers in place of lower level ones, but 5e doesn't really have an analogue for that either.)I loved the epic destinies of fourth edition and would love to see that return and this actually seems like a step in that direction.
To emulate that in 5e, it sounds like you would want "feat packages" or "boon packages" - so building on the current DMG approach with new feats/boons that emulate some of the key epic features that you want to carry forward into this edition, arranged in thematically unified bundles.