my probability that something like string theory is true would go way up after the detection of a Higgs boson

I'm not sure that this should be the case, as the Higgs is a Standard Model prediction and string theory is an attempt to extend that model. The accuracy of the former has little to say on whether the latter is sensible or accurate. For a concrete example, this is like allowing the accuracy of Newtonian Mechanics (via say some confirmed prediction about the existence of a planetary body based on anomalous orbital data) to influence your confidence in General Relativity before the latter had predicted Mercury's precession or the Michelson-Morley experiment had been done.

EDIT: Unless of course you were initially under the impression that there were flaws in the basic theory which would make the extension fall apart, which I just realized may have been the case for you regarding the Standard Model.

What would a graph of your trust in mainstream modern physics over the last decade or so look like? And how 'bout other academic fields?

my probability that something like string theory is true would go way up after the detection of a Higgs boson, as would my current moderate credence in dark matter and dark energy

One of these things is not like the others, one of these things doesn't belong.

Lots of physicists will acknowledge that string ‘theory’ -- sorry, I cannot bring myself to calling it a theory without scare quotes -- is highly speculative. With 10^500 free parameters, it has no more predictive power than “The woman down the street is a witch; she did it.”

On the other hand, there's no way of explaining current cosmological observations without recurring to dark matter and dark energy (what the hell was wrong with calling it “cosmological constant”, BTW? who renamed it, and why?), short of replacing GR with something much less elegant (read: “higher Kolgomorov complexity”). Seriously, for things measured as 0.222±0.026 and 0.734±0.029 to not actually exist we would have to be missing something big.