Are you matching beta or VBE?
Touching the transistors to put them in the breadboard then takes time for them to cool off.
Using a high test current heats them up, this is the most frustrating because readings are always moving.
Add some capacitance like 0.1uF to prevent RF pickup from getting amplified, which also makes readings wander.
A box to prevent convection currents, drafts, heating system, sunlight, IR etc. helps.
I don't see a point to super-matching (<2%) because your end circuit will have thermal gradients and they'll end up running at different temperatures anyway. Like in an audio power amplifier. You can apply heat-shrink to a diff. pair though.