Warlock chassis is the way to go, I think. You get full caster progression, but not full caster volume, which fits for a class that mostly uses a weapon but mixes in some spells.
Focus on bladetrips (a la BB/GFB) as primary offensive option. (They did originate with the 4e swordmage, after all). Make a bunch of new ones for other damage types, mixed in with other soft control options. Give Bladesinger Cantrip + Attack as the Tier 2 offensive boost; it roughly tracks with the expected Warlock damage output of EB+AB.
Ability to "smite" with a bonus action use of a spell slot, turning offensive spell into hit on next melee attack. (This mechanic has been done in multiple swordmage-type homebrews, the mechanic isn't hard to derive.) Possibly other uses for BA derived from subclass.
Invocation budget can be used to strengthen martial or magical identity, or gain utility, as desired. Turn Mystic Arcanum into flexible "high-tier" invocations, of which gaining a 6th-9th level slot is only one option.