We investigate models of self-consistent chemical enrichment of the intergalactic medium (IGM) from z = 6.0 -> 1.5, based on hydrodynamic simulations of structure formation that explicitly incorporate outflows from star-forming galaxies. Our main result is that outflow parametrizations derived from observations of local starburst galaxies, in particular momentum-driven wind scenarios, provide the best agreement with observations of C IV absorption at z similar to 2-5. Such models sufficiently enrich the high-z IGM to produce a global mass density of C IV absorbers that is relatively invariant from z = 5.5 -> 1.5, in agreement with observations. This occurs despite continual IGM enrichment causing an increase in volume-averaged metallicity by similar to x 5-10 over this redshift range, because energy input accompanying the enriching outflows causes a drop in the global ionization fraction of C IV. Comparisons to observed C IV column density and linewidth distributions and C IV-based pixel optical depth ratios provide significant constraints on wind models. Our best-fitting outflow models show mean IGM temperatures only slightly above our no-outflow case, metal filling factors of just a few per cent with volume-weighted metallicities around 10(-3) at z similar to 3, significant amounts of collisionally ionized C IV absorption and a metallicity-density relationship that rises rapidly at low overdensities and flattens at higher ones. In general, we find that outflow speeds must be high enough to enrich the low-density IGM at early times but low enough not to overheat it, and concurrently must significantly suppress early star formation while still producing enough early metals. It is therefore non-trivial that locally calibrated momentum-driven wind scenarios naturally yield the desired strength and evolution of outflows, and suggest that such models represent a significant step towards understanding the impact of galactic outflows on galaxies and the IGM across cosmic time.