I will give you my own perspective based on what I have seen and discussed with others in the industry. The carbon equivalent formulas were originally developed based on evaluating the effects of alloy addition to crack susceptibility of the base metal HAZ. Lab tests were conducted on weld coupons to correlate the application of preheat with base metal composition to susceptibility of crack initiation and propagation in the base metal HAZ. So, depending on the melting practices used for the steel, the carbon equivalent formula can be tweaked to provide a better fit with lab data for a particular family of steel compositions.

There are several versions of carbon equivalent formula's that were developed specific to the families of steel – low carbon low alloy, C-Mn, C-Mn-Si, etc. For example, the CE formula applicable to low carbon steel does contain the Si term, although this contribution has a very small effect on the total CE and subsequent preheat requirements because of the size of the denominator.

For C-Mn low alloy steels, the CE (IIW) formula is generally accepted. The ASTM committee felt that this formula being more readily accepted should be endorsed in A-6.
AWS is responsible for their standard and decides on their use of a CE formula. Since I deal with ASME B&PV code steels, in QW-403.26 Section IX, the CE formula accepted by ASTM A-6 is used.

I remember reading something quite similar, probably here and probably written by you, after my initial inquiry.  What I haven't been able to do is determine what steels make up the "family" associated with the ASTM A6 formula.  ASTM A6 does list a number of steels, but as far as I can determine the Si content of these is in the same range as the steels we usually use in bridge construction, ASTM A709.  In addition, the welding code, D1.1, is intended for general use and is not bridge specific as the D1.5 version is.  Both the D1.1 and the D1.5 codes use the same C.E. formula, and as I said earlier, this formula contains an extra term for Si.

If you could point me to a reference enumerating the steels acceptable to the ASTM A6 formula, that would be a big help.  Thanks for everything.

http://www.matter.org.uk/steelmatter/manufacturing/6_3.html

this is the standard CE formula that I have seen used
C + Mn/6 + Cu/40 + Ni/20 + Cr/10 + Mo/50 + V/10
I've never seen Si included in there.
I believe the intent is just to account for trace ammounts of effective carbon present as result of the additional alloying elements. This is important to determine if a steel has high propensity for cracking after welding. The CE threshold may vary for different applications. I typically see maximum allowable value of 0.40 in specifications I work with.
another note worth mentioning, don't use nominal specification values when calculating CE. I typically run this formula using actual values reported on mill certification for the heat of steel that we are welding.

I use the following CE formula from the IIW for cast steel:

C.E. = C% + Mn%/6 +  (Cr%+Mo%+V%)/5  +  (Ni%+Cu%)/15
                                     

API RP577 has the following formula

CE =C+Mn/6 + (Cr+Mo+V)/5 + (Si+Ni+Cu)/15

in section 10.9 and talks to the reason why it's important,

Cheers

Rob