Regarding the correlation between cap strength and convective mode... I think it's a slight misconception to think that a weak cap will always yield linear convection, while a strong cap will yield supercells. The mode of convection depends upon many things -- strength and 'shape' of forcing, etc. Imagine it as a continuum box:
WF - WC --------------------- WF - SC
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SF - WC --------------------- SF - SC
where WF = weak forcing, SF = strong forcing, WC = weak capping, SC = strong capping...
Now, in cases of strong forcing (say linear too) and weak cap, there will be a great tendency for MCS / linear development, and in cases of weak forcing and strong cap, there may very well be no convective development (cap bust)... The rest of the possible combinations of forcing and capping yield the many different tendencies, beit mostly discrete cells or mostly linear convection.
Why do I not think cap strength alone has too much to do with convective mode? Even when you have a weak cap, you still need convergence (forcing). You can have no cap and still not have convection. Likewise, even if you have a really strong cap, you can have widespread convection if the forcing / convergence is high enough to overcome the convective inhibition.
Of course, it's important to remember that many other factors play into this... For example, the orientation of the shear vector relative to a boundary providing convergence ... Shear vectors perpendicular to a boundary (presumably, the boundary is providing the convergence) will tend to yield discrete cells, while shear vectors parallel to the boundary tend to yield convective seeding and MCS development...
Now, back to the topic.... The strength of the cap is a function of the temperature (technically, virtual temperature, but lets start basic) difference between the parcel and it's environment, assuming the parcel is "cooler" than the environment. Now, lets just say, for simplicity, that the atmosphere does not change through the day except for the surface layer. Now, lets say we warm and/or moisten the surface parcel. This will effective reduce the strength of the cap since the parcel will have a "warmer" temperature than it had before -- so, relatively, it is less cool than before, and thus the strength of the cap is weaker. Now, in the case of moistening the parcel (say, via increasing the dewpoints), the parcel attains saturation at a lower level (it's lifted condensation level is lower), and thus it cools at a slower rate (moist adiabatic -- ~5.8c/km -- vs. dry adiabatic -- 9.8 C/km). So, above the LCL level, and below the level of free convection, the moistened parcel will be 'warmer' than the previous unmoistened parcel. Now, in the case of increasing the temperature of the surface parcel, semi-obviously, if you raise the original temperature of the parcel, the parcel at a particular level below the LFC will have a higher temperature than the non-heated parcel would have...
So.... On a normal summer day east of the Rockies, given insolation (incoming solar radiation -- aka the sun is out), the surface tends to both increase in temperature and moisture (via evapotranspiration -- moisture from plants), and thus the relative cap strength tends to decrease. Now, remember that the example in the previous paragraph assumed that we kept the atmosphere of alone save the surface. Obviously, it is seldom that the temperature and moisture profile of the atmosphere above a given location doesn't change at all in a 6-12 hr period. However, also remember that solar radiation impacts, largely, only the lowest portion of the atmosphere (say, the lowest couple of km). There are other important processes, however, that should be accounted for to get an accurate forecast of the temperature/moisture profiles -- such as subsidence (which tends to warm the 500-850mb layer), synoptic-scale lift (which tends to cool the 500-850mb layer), upwind mid-level precipitation (which tends to cool the 500/700 - 850mb layer). Yes, there obviously are exceptions, but this is a simple explanation / example...
So... How to do this with only the typical 2-launch day? Well, first off, on a "big days", NWSFO's tend to release special 18z soundings, which usually help a great deal in determining cap strength a few hours before the typical convective initiation time of late afternoon (again, when the temperatures are usually highest, and thus cap strength, with all that we are assuming, is weakest). A lot of times, model data is used to help shed light on forecast cap strength. Othertimes, since the mid-upper levels TEND not to change drastically in 6-12 hours, 12z soundings can be adjusted for the forecast afternoon surface temperature - dewpoint.
Much of this is best seen on skew-T log-P charts... Since I don't know your level of meteorological knowledge, I apologize if you find anything above obvious and are offended. Likewise, if the above is still confusing, I'm sure Mike G (the "links guy"), can post some good websites about skew-t log-p charts.