Though I can agree with the general perception on the Arcane Archer, there is no need to severly edit the Arcane Archer.
Considering the Eldritch Knight approach, you could simply flavor the Eldritch Knight as an archer (fighting style, feats, etc.) and work with your DM so that instead of picking spells exclusively from the Abjuration or Evocation schools, you rather pick spells from any schools (even other spellcasting classes) that could be reasonaly thought of being "cast as an arrow" and/or duplicating one of the Arcane Shots; for example, beguiling arrow becomes charm person, bursting arrow becomes ice knives, etc.
The Dungeon Dudes and Treantmonk (among others) posted videos about the Arcane Archer. The Dungeon Dudes do a good critique of the class, and the main weak points they identify is 1) the limited number of arcane shots and 2) the fact that the shot does not apply to crossbows (which I think is not the right way to look at this). One suggestion is to increasing the number arcane shots learned, available and of uses per day (based on the Proficiency bonus, maybe), so that it is more "equivalent" to the number of maneuvers uses a Battlemaster can use in a day. Increasing the damage of some shots at higher levels could also be considered (11th and 18th for example). As an alternative, yhey also suggest to reflavor the Battlemaster to be a "better Arcane Archer".
This Treantmonk video and this one mechanically discuss the subclass, the various arrows and a recommended build. One main comment is the small number of uses (2/SR), and the fact that the ST DC for the shots is set using Intelligence. He suggests that the number of uses per SR should scale with level (with proficiency, or following the number of Arcane Shots). Also, picking arrow shots that does not require a ST is probably the way to go. The second video actually discusses an Arcane Archer build to show how to use them effectively, showing that the subclass is actually better than most think.
- Banishing Arrow is effective;
- Beguiling Arrow might be the worst;
- Bursting Arrow has no ST and is AOE, thus not too bad;
- Enfeebling Arrow is one of the weaker option;
- Grasping Arrow, though is uses poison damage, it is still the best arcane shot available (no ST for the additional damage effect when target moves or is forced to move), better than many if not all Battlemaster maneuvers ("This is unreal!");
- Piercing Arrow is worst than Bursting Arrow;
- Seeking Arrow is among the worst, pretty niche in its usefulness but could still be useful;
- Shadow Arrow is middle of the road.
Essentially, the build uses VHuman with Sharpshooter, initally selecting Grasping Arrow and Banishing Arrow (the "best" second option), and later Bursting Arrow, Shadow Arrow and Seeking Arrow (in this order). Using the Piercer Feat for additional damage with the arrow and the Telekinetic Feat to force Grasped targets to move and generate more damage with this shot (suggestion from myself to consider: Magic Initiate/Fey Touched/other to select the spell Hex to reduce the chances of the target from escaping the Grasping Arrow).
Overall, the proposed build delivers more DPR than his baseline and a "straight" fighter using Crossbow Expert (starting at 7th level, per his calculations).