GaAs-based broad-area diode lasers are needed with improved lateral beam parameter product (BPPlat) at high power. An experimental study of the factors limiting BPPlat is therefore presented, using extreme double-asymmetric (EDAS) vertical structures emitting at 910 nm. Continuous wave, pulsed and polarization-resolved measurements are presented and compared to thermal simulation. The importance of thermal and packaging-induced effects is determined by comparing junction -up and -down devices. Process factors are clarified by comparing diodes with and without index-guiding trenches. We show that in all cases studied, BPPlat is limited by a non-thermal BPP ground-level and a thermal BPP, which depends linearly on self-heating. Measurements as a function of pulse width confirm that self-heating rather than bias-level dominates. Diodes without trenches show low BPP ground-level, and a thermal BPP which depends strongly on mounting, due to changes in the temperature profile. The additional lateral guiding in diodes with trenches strongly increases the BPP ground-level, but optically isolates the stripe from the device edges, suppressing the influence of the thermal profile, leading to a BPP-slope that is low and independent of mounting. Trenches are also shown to initiate strain fields that cause parasitic TM-polarized emission with large BPPlat, whose influence on total BPPlat remains small, provided the overall polarization purity is >95%.