I guess I'll be the voice of reason, or disssent, or whatever.
Why not work on performing the calculation faster in your head?
The OP sounds like a reasonably smart chap. I supposed he could have some learning disability or something. But barring that, he could work on doing math faster in his head, which is one of the things RPGs tends to encourage improvement in.
Barring adding up multiple dice larger than a d10, adding numbers 10 or less together should be mentally ingrained, like multiplication tables.
You should know 3+8=11 by rote, not by counting apples in your head.
From there, sort the dice into piles that add up to 10 with one remaining pile of the spare dice that didn't make up a whole 10. Your eye-brain system should automatically be able to count the piles to see there are 3 piles of 10s, and a small pile adding to 7, telling you the total is 37.
As part of this process, of sorting the dice, your brain should automatically spot combinations that add up to 5 or 10, to aid in rapid sorting of the dice. Pair up 2's with 3's, 6's with 4's, 1's with 4's, and you'll quickly sort out the pile into 10s and the remainder.
As for adding the bigger numbers in your head (like the total of the dice plus the modifier), there's tricks for that as well.
Add up the 10's digit seperately from the 1's digit. So if we need to calculate 37 + 14, we would do it in our head as follows:
doing the 10's digit: 30+10 = 40, remember that.
doing the 1's digit: 7+4 = 11
combining the two values: 40+11 = 51
In this way, you're not trying to do old-school adddition on the chalkboard where you add the 7+4, write down the 1 from the one's digit of 11, and carrying the 1 from the ten's digit in 11 to then add 1+3+1 and writing 5 next to the 1 at the bottom. It takes that much verbiage to explain what's happening mentally. the other way is simpler to handle the operations in your head.