Now I'm curious what guidance might look like 

I've played in games that tried 2d10 as well as dice pool games like shadowrun fate & modiphius' 2d20 systems & the 2d10 winds up feeling particularly bad as you have bob with two same colored dice who either slows the game rolling one by one or always seems to roll high low but never low high, meanwhile everyone else has the added frustration of "if only I had said blue was tens instead of green" or whatever on top of the chance for bad rolls. A dice pool is good, but the system needs to be designed for it & expertise dice are a nice middle ground between 1d20+mods & the kind of fluid opposed rolls you tend to see with combat in dice pool systemsOK, now the actual post.
I once suggested 2d10 on reddit and got downvoted to oblivion. I personally kind of like the idea, since even a teensy curve is better than total randomness. The only real issue that would need to be addressed is critical hits, which would be bit rarer. As crits are especially useful to paladins and rogues, this could possibly be addressed entirely in a feat (perhaps one with a higher-level prerequisite) that would allow anyone to increase their crit range by 1.
The expertise die, however, is not really "half-assed." Something like it is already used in D&D: guidance, resistance, and bless already grant an additional d4, as do House abilities in Eberron. Something akin to the expertise die was suggested, IIRC, in an older UA, although I can't remember which one or how it was implemented.
The expertise die isn't one where you can't roll until you know the modifiers because the modifier is simple enough that you could record it on your sheet. At worst, you have a case where you would make your roll and half an hour later suddenly exclaim, "Dammnit, I had a d6 expertise die, not a d4." Which is no different than "Dammit, I had a +4, not a +2."