An Open Analysis
So I realize diana has a built in 20% attackspeed passive such that she doesn' need to build attack speed items to make use of her passive. Thats not to say it can't work well to go with attack speed on her. But would have to be versus the right matchup where your enemy won't be so hard to catch and where they don't wombo combo you so much. or not versus say an irelia who would love to 1v1 you with sustain. I soon discovered that going with attack speed you need two things, first you need some survivability since it takes some time you can't just go in drop pay load an run out...And second you pretty much have to get mercs as a melee champion. since when your in the thick of it your gonna get cced a lot and won't benefit from your attackspeed. Or face enemies with little hard cc. Lets just say facing bard, irelia, another diana and a brand didn't help since they stunned a lot. Then I thought wouldn't it be great there was a nashor tooth like zephyr that had tenactiy. Then I thougth mhhh well if i have zephyr going gunblade would make sense. Lastly to kick things up a notch I had this idea for critical strike boots the other day: The boots would give 25% chance to crit. However crit would not do 200% of your damage. instead they'd do 200%-30% (or minus whatever number would be reasonable such that the boots would be as cost effective as zerker grieves at 1000gold)
So I put this build together:
the 25% crit boots 
I think that'd be pretty cool.
I realize diana only scales with ap. But if you look at two ad items i'm using. one gives a lot of utility tenacity cdr attackspeed all in one and just 25 ad. the other provides sustain active slow etc. and the boots help complete the synergy by putting all that attack speed to good use.
now with regards to critical chance. This recent thread has had countless replies But I think there's a pretty simple solution: It goes like this.
A common suggestion to change critical strike is to flatten its damage.
To quote Riot Reinboom (NA) Flattening the output. (Flattening the output is where Critical Chance becomes a basic attack damage multiplier. 1% Crit -> 1% Basic attack damage amp).
I think a comprimise between the two would work nicely. A mixture of flattening and the other half would keep the current crit behavior.
So, if you have 100 damage, at 25% crit chance each of your attacks will do 125 damage. Instead of having 1 in 4 hits doing 200 damage and the rest 100.
So the 50/50 solution would go like: at 25% crit chance your base damage = 100 100 times 200% = 200 200/4 = 25 25/2 = 12.5 so your autos deal 112.5 A crit = 200 – your AD 100 = 100 100/2 =50 so 112.5 plus 50 = 162.5. so the new max crit would differ by 200-162.5 = 37.5 dmg. from the traditional/current crit.
Now with crit boots that reduce crits to .70%
lets say you have 200 ad 200 times 1.70% crit dmg since boots reduce dmg by 30%.
340 = crit at 25% crit chance you divide the difference by 4... so : 340-200=140 divide by 4 = 35 thats the amount your autos would do if crits were flattened.
applying the 50/50mixture: 35/2 = 17.5 autos now deal 217.5 70% of damage... .7 * 200 / 2 =70 217.5 + 70 = 287.5 dmg (17.5 x 3) + 87.5 = 140 checks out.
these boots would also come in handy for manaless champions who may want a similar effect to sheen procs without having to buy mana. Sheen sort of simulates the effects of having 25 to 33% crit chance. which these boots would come close to replicate.