Would love a half-caster arcane gish (#1). I think the paladin offers a starting point. Heck, the oath of vegeance paladin is 85% of the way there.
Maybe geomancer whose spells/abilities change depending on the current terrain?
I have to say I agree with your instincts on the Paladin-based approach. In one of the last 3.5Ed campaigns I was part of, I ran a LG "Arcane Paladin": Antares Whitechapel, Sword of Thoth, of the Illuminated Society of Thoth was mechanically designed as a Marshal/Duskblade/Battle Sorcerer. So he had some spells, of course, but importantly, he also had "Auras" that helped out his party mates.
Was he as powerful as a single class Paladin? Nope. Was he fun as hell? Yep. Did he feel like an Arcane Paladin in play? Oh yes, very much so.
Geomancer, though...I love them- played one shortly before Antares, in fact- but I don't think they really would form a good basis for a pen arcane Gish half-caster.
Geomancer Drift mechanics might, however, be a good way to model someone who is a bit reckless with arcane research...
Nearly everything being proposed, to me, sounds like things that can be done as archetypes of existing classes.
The only exception, that I see, would be an arcane half-caster en par with the paladin (clerical) and ranger (druidic) half-caster fighter-types.
The bladesinger (in addition to being created and intended strictly for FR, and for elves) and swordmage gives you a magic-user with a little sword-skill/play. The Eldritch Knight does this same thing from the reverse side of the street: a fighter with a [purposely] little bit of spell/arcane magic capacity.
The possibilities for that character type with a Bard or [Blade] Warlock both OVERshoot the target. Bard, as a FULL caster and Warlock with very specific flavor magic powers (if not the spell count/progression) built in.
As the game is set up now the fully "half," middle of the road, [arcane]caster/warrior isn't presented [without multiclassing, precisely, one level of Fighter to one level of wizard].
Generating a full new class requires, not just that the archetype can't be portrayed in some fashion with existing classes, but it's own signature mechanic/features/ability that other archetypes don't already use. If a proposed "class" just uses existing mechanics...and the rest of a matter of RPing flavor...then that's not a case for developing a full separate class...to me.
So that's the only choice/option I see that the fantasy roleplaying game of Dungeons & Dragons is missing/still needs: Arcane Half-caster Warrior type guy.
Wanting a pokeman, wanting a jedi, wanting these other things I'm seeing listed here...sure, you can flavor things this way or that to get a character like that...and ROLEPLAY it how you like. But if you want to play an X, from genre/game/film/cartoon/comic Y, when D&D is built to play genre A,B or Z, then why play 5e D&D?
This is near the top of my list. Seems to be a missing niche.
Names for the class and 2 subclasses![]()
Ok make Hexblade a 4th subclass)I'd love to see a Ninja class. One that combines stealth with acrobatics.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.