You've got a few options. If you want to keep your DPR up, a Rogue multiclass works pretty well, e.g. Sharpshooter EK 11/Swashbuckler 9. (Whether you go EK first or Swashbuckler first will vary based on what playstyle you prefer.) That gives you at-will ranged damage about as good as a regular Sharpshooter EK 20, possibly better against high-AC foes. You miss out on the extra action surge but have lots of ability to hold the range open, get some nasty sneak attacks to go with your SCAG cantrip War Magic, and get to play with Panache for awesome single-target crowd control that bypasses legendary resistance and is fully compatible with Cunning Action (Hide), because the target doesn't need to be able to see you to be taunted; hearing is sufficient.
Another fun combo is EK 11, Rogue 2, Necromancer 7. You're a 10th level caster with up to 4th level spells. The point of this build is to exploit three things: the way skeleton archer damage scales with proficiency bonus, the synergy between Greater Invisibility (or Fog Cloud/etc.) and Cunning Action (Hide), and Eldritch Strike + Bestow Curse V. Even before you factor in the skeletons, your DPR is almost as good as a real EK 20, and your spell list isn't quite so narrowly-focused on abjuration/evocation: you have more room for defensive spells like Blink/Blur and rituals like Find Familiar. If you invest in the Skulker feat you can do fun things like snuff out all the torches and then Vampiric Touch + Cunning Action (Hide) every round from enemies relying on darkvision, since darkvision only replicates dim light and Skulker lets you still hide in dim light. In short, you wind up with a character who can be either the anvil (when he's spending all his spell slots on a huge skeleton army of longbowmen) or the hammer (when skeletons aren't feasible and he spends his slots on personal enhancement and mobility).
Honorable mention goes to EK 8/Warlock 2/Swashbuckler 10 for highest personal DPR, but I don't like it all that much because: (1) it's MAD with the extra Charisma dependency, (2) the damage output isn't all that much higher than a regular EK 20, (3) it feels gimmicky to me. The damage ends up being worse than the Necromancer variant against most enemies, especially in a party that has some way to generate advantage at range (e.g. someone casting Conjure Animals to summon constrictor snakes to restrain enemies).
Final observation: for a Mobile Sharpshooter EK 8+, the best (most fun, IMO) use of War Magic is to toss a net (PHB 148) from 10' range over an enemy, restraining them so that you get advantage on your subsequent Booming Blade cantrip attack on them, then back up either 35' or just 5' afterward (depending on terrain and tactical considerations). If you back up 5', then is at least a chance the enemy could still attack you on his turn (if he has Multiattack with a slashing weapon, he could spend one attack getting free and the other attack(s) on you) but even then he takes Booming Blade damage for moving. (BTW, I hate the name Booming Blade and at my table it is False Fetters: conjured shackles made of air which explode concussively if stretched too far.)