Pretty much every attempt I've seen to make Gish or Gishlike character class has used the Fighter as the base and then added on spellcasting. Whether that's an Eldritch Knight in 5e or a 4e Swordmage or the massive variety of 3e Prestige Classes that require 3 levels of fighter and 3 of wizard before you get to play what you -wanted- to play at level 1.
And it occurred to me that we largely do it that way for two reasons:
1) Githyanki Silver Swords
2) Paladins
... but what if that's the wrong way to do it?
4e situated the Monk as a Psionic Striker and put out a Battlemind in plate armor with a shield and sword. And over in the Leader category it had the Ardent with platemail and a greatsword.
But what if the right way to do a Gish in 5e is to use the Monk chassis instead of the Fighter and then do a Wizard/Monk Psychic Warrior in the same vein as a Cleric/Fighter Paladin?
Give them martial weapon proficiency and light armor but allow them to us Intelligence in place of Dex. And allow them to "Spellstrike" with cantrips at level 1+, using the weapon's damage dice and the cantrip's damage type. So a 2d6+Str fire damage greatsword swing because you used Firebolt to spellstrike, secondary effects apply normally. So a Ray of Frost spellstrike slows your enemy down or you can give them a 1d4 penalty on their next save with a Mind Sliver spellstrike. And then, as a bonus action, make a follow up attack whenever you use a spellstrike to deal an additional 1d4 damage of the same type, like a monk does with their bonus actions but you don't have Ki to get a second attack.
But also give them the Dash/Dodge/Disengage bonus actions of the Monk. Because the Wizard/Monk Gish is still a d8 light-fighter rather than a d10 "Stand in Melee wearing Plate" kind of fighter. And at 5th level when they get Extra Attack let them spellstrike with two different cantrips if they like. And, of course, they get spells they can cast as an action -instead- of fighting in melee with spellstrikes and the like... But like paladins: half casters. Of course eventually they get to cast a spell and make it a melee attack in a true "Spellsmite" or something, which replaces the use case of stunning strike for Polymorph or hitting an enemy to apply Enemies Abound rather than them getting a save.
Sorcerer/Rogue for a different type of Gish that still focuses in on high mobility, but instead of bonus action dash or disengage they bonus action teleport up to 20ft or something similar. And rather than sneak attacking and spell points they get a dice pool they can try to add to their spellstrike's damage (if the target is threatened and/or they've got advantage or whatever) -or- use to alter the function of their spells.
How about a Warlock/Barbarian Gish that is really just some kind of Arcane Monstrosity class where your patron gives you Physical Power through mystical transformation rather than spellcraft? You still get Invocations, though, and Green Flame Blade or Pact of the Blade or whatever to maintain the occult connection. Instead of Rage reducing the damage you take you still get the d12 hit dice and big armor that may or may not be magically bound to you or something.
I dunno... but it could really increase the flavors of gishiness beyond "Spellblade" if different methods of being a gish created different playstyles while playing with the same basic concept. Magic + Weapon.