Are there any systems or experts that factor in "intermediate" cards in deciding when to bid?
The most accurate system I have seen for notrump bidding is a 5-4-3-2-1 count for the cards Ace through 10. This of course is a base 60 for the whole deck instead of 40, but can easily be normalized by doubling and dividing by three. (Round 2/3 up and 1/3 down.) With a little practice this is barely slower than the standard Work point count.

Not the assumption here of notrump - the Work 4-3-2-1 point count overvalues aces and kings for notrump play. 

Although this system is no better for suit play than the standard Work point count, it is perhaps no worse. Aces and Kings are undervalued as a disadvantage, but counting 10's for something is an advantage. One possibility for restoring the true value of Aces and Kings (in suit play) might be to add (Quick Tricks - 1.5) to the count above in that circumstance. (The 1.5 comes from the Quick Trick strength of an Ace and a King in separate suits, which is an average holding.)