We all know Elise and Diana didn't do so hot in your first forays into trying to make AP fighters since they could do too much damage while building tanky
I really don't think that was the issue in either case.
Nasus and Volibear exist.
There's a clear archetype of tanky DPS that build tanky and deal DPS. Those are called fighters. Dealing damage while building tanky is what tanky DPS champions do.
Generally speaking such fighters aren't really AD or AP either, they tend to deal very hybridized damage, and for their single damage item - they tend to gravitate to things like 
None of which are specifically AD or AP, and tend to be independent of AD or AP in terms of how they function. Often scaling with levels, the levels or opponents, or some other aspect of game time independent of actually dumping gold into damage.
The problem is, most AP "fighters" right now are actually just built as assassins, with only Jax and Kayle really fitting the bill for fighter.
~40% of fighters tend to be like Nasus. Fighter/tank, gets damage for free and builds full tank.
~40% of fighters tend to be like Yasou. Fighter/assassin. Gets a solid defense mechanic (often for free) that's completely independent of defensive scaling, so they can build glass-cannon while still functioning as tanky DPS in a short burst.
A lot of fighters are built as assassins if they fall into the fighter/assassin category, because that's just how things work out for optimal build patterns there.
If you're limited to a singular, easy-to-counter damage type heavily reliant on building damage to deal respectable damage, and if you have a limited-time defensive steroid that's pretty solid despite building glass-cannon, you're going to build glass-cannon.
For a solid AP fighter I'd probably look more at Singed and especially Rumble, as they tend to walk a line where you actually build them 50% damage, 50% defense and they do play more into the AP path than a hybrid one.
Diana can also do it if she builds Nashor's Tooth, but that's considered a sub-optimal build compared to her assassin build.
Diana's to easy to counter-build for her to get away with going more the hybrid/tanky DPS build strategy.
Unlike Nasus, you can just build BV against her as a squishy for your single defensive item and pretty much ignore Diana if she trys doing cutesy AS things.
Also - if you want to stand next to something and AA them plenty of times, you want a kit more like Shyvana's where you just build full-tank so you can survive long enough to do that.
AS builds are only really solid in a 1v1 situation on a melee champion. Once you have to worry about slowing fields, any type of CC tanking your DPS to 0, and the capacity for a team to 100%-->0% a wide range of assassins mid-leap by 4 members bursting 25% of their HP each, standing next to things to AA them to death is really sub-optimal on a glass-cannon.
You want range or defense to do that - it doesn't really work with mobility alone.
Any thoughts?
I don't see an issue with Diana being a fighter/assassin that builds glass-cannon and erases things.
1 issue with her fighter/assassin playstyle though is a very hamstrung reflexive/tactical path of playing against Diana though (most fighter/assassins and assassins suffer from this).
Specifically with Diana: if she does enough damage to start her combo with her ult rather than trying to mark a target for 2 ults, there's not much you can do against her.
She gets within 825 range of squishy, squishy dies.
