2d10 - Thing to Try

I stated to my group that I had an Experiment I wanted to perform when next I ran.
This was answered by very loud eye-rolling from several.

But this is not how I would like for my precious readers to respond. If I write about a thing I would like to try and game, please, dear readers, try to ask me about it after a month or so.

Basically, I want to run a session or two rolling 2d10 for checks where we would otherwise be rolling a simple d20.
The object of this is to yield a bell-curve of probabilities, thereby eliminating the manic crit/fail dichotomy which has become central to D&D and the d20 system. The d20 is a capricious god, and it has been thoroughly fetishized. This becomes apparent if you look at a handful of captioned DnD memes.
In fact, if an aspect of the game has become meme-able, I probably want to destroy, decanonize, or undogmafy it.((alignment, magic missile and cat pictures shall be purged))

By introducing a bell-curve probability, I expect players to be able to decide on actions and make plans with reasonable expectations, rather than trusting to chance or having an otherwise reasonable plan fail for no apparent reason.
Also, crits and fumbles seem to come in streaks, and it becomes taxing to the Game Master of come up with explanations for all these extreme happenstances.

Some things to note:
Difficulty classes need to be adjusted.
With 1d20, there is a 5% chance of rolling a natural 20.
With 2d10, there is a 1% chance of a natural 20. So the DC of 20 would become equivalent to 18 or 19.  See spreadsheet

Skill Modifiers become more significant. As the DCs become numerically lower, without making any other changes, the modifiers or bonuses to a roll make a larger difference to the outcome. If the rounding in the conversion above seems stingy, the reason is to balance out the increasingly significant modifiers.
The range become 2-20. 
The chance of rolling 2 is 1%. At this rate, I am ok with still using fumbles and crits. It will bring back the spark back, I'm sure.
With Combat criticals, maybe adjust the crit range.
The rules as-is specify that if an attack succeeds and is inside of a weapons crit range, then the player must roll again and hit in order to get a succesful crit. So to keep critical hits from becoming extinct, maybe eliminate that second roll, or adjust the ranges crit ranges using the chart above. A crit range of 20 becomes 18-20. 19-20 becomes 17-20 and so on.

I am concerned about the scaling of Difficulties and Armor Classes over 20. I'm not sure how to work that out. For now, I will just scale it linearly and see how that works.

I expect to be able to run this in the next month or so. The beauty of our current schizophrenic campaign is that it allows for lots of experimentation. So if bell curves are no fun, it won't hurt much.