Update:
End update.
The Builds:
Post #2: Str-based Bladeforged
Post #3: Str-based Human with Wraith form
Post #4: Int-based Warforged with Harper
Post #30: Int-based Half-elf with harper, fire specced in divine crusader
These are all arcane melee builds that utilize some combination of kensai, stalwart defender, and eldritch knight. The first build, and probably the strongest overall, is a str based bladeforged which invests heavily into the racial tree for communion of scribing and power of the forge. This build probably has the highest dps and best self healing with two quickened reconstructs available. The second is a str based human that invests heavily into pale master for wraith form. This build will have lower base dps, comparable burst dps, healing over time with weaker burst healing, and lower damage mitigation with higher damage avoidance. The third build is an int based warforged that invests in harper for int to hit and damage, know the angles, and versatile adept. I'll give each build it's own post below. Please let me know if you see any errors. As always, any and all feedback is welcome. Thanks in advance.
My Reasoning:
With the recent changes to kensai, eldritch knight multiclass builds now have easier access to crit enhancements. In the past, I had considered an eldritch swashbuckler, but was never pleased with the results. The synergy just wasn't quite there. Kensai, however, has introduced some decent options. It may not even be fair to call these builds eldritch kensais because I don't invest heavily into eldritch knight. Although there is some decent low hanging fruit, the higher tiers are simply not worth the investment imo. Nevertheless, these are all arcane melee builds. Spells are used primarily for buffs and convenience, but there are a few no-save damage spells as well. These are definitely not uber endgame builds. At this point, I haven't played any of them so it's all still theory-crafting. On paper at least, they should perform just fine even in EE content. I probably wouldn't take them into LE though (well, maybe one of them if properly maxed out).
My initial assumption was to go int based and use harper for int to hit and damage as well as undead form for the self healing. This proves to be rather difficult, however, as AP can get spread pretty thin. Here are the basics I started with for each of these builds:
~32 minimum in kensai and at least 6 fighter levels for one with the blade (20 melee power), keen edge (+1 crit range), and strike with no thought (+1 crit multiplier)
~13 minimum in stalwart defender for defensive stance (25 PRR/MRR) and tenacious defense (+20% hp)
~13 minimum in eldritch knight for improved shield (10 PRR) and arcane barrier (take 25% less damage for 20 seconds when below 50% health)
With these basics, that only leaves 22 AP. Self healing is essential and, on an eldritch kensai, that's either going to be repairs on a warforged/bladeforged, or undead form on a fleshy. With this in mind, I came up with three different variations. I built each of them for THF because that's what I want for my next build, but each of them would work equally well with SWF. Just swap those feats and you're done. A sword and board arcane melee would probably have quite a few differences from these builds (e.g. shield mastery feats and invest in vanguard), so these builds may not translate well into that fighting style. I wouldn't build a TWF arcane melee because there is less synergy with cleaves and it would spread stats thin.
EDIT: unbongwah pointed out the possibility of going int based with harper and using divine crusader for healing. The half elf version is the result of that.