I don't want this to sound like I am actually encouraging this pursuit, but here is one way to match the devices for beta and Vbe at the same time.
It requires a bunch of precision resistors, + and - power supplies, and a pile of transistors.
First connect 10 or 20 transistors together at their emitters. So this voltage will be the same by definition. Connect each individual base to ground through a precision resistor (20-100k). Then connect each collector to the appropriate supply (negative for PNP, positive rail for NPN) through individual precision resistors (say 2k). Then connect the common emitter through a low value resistor to the other supply as appropriate (plus for PNP, minus for NPN). Size this common emitter resistor, and voltage it is connected to for the test current you want times the number of devices. So if you want 1 mA in each of 20 transistors you will want 20 mA total supplied at this common emitter node.
With all the emitters tied together, they will share the current between them based on the individual differences in Vbe. Further the resistor in series with the base will give you a direct reading of beta and further influence the current sharing. With a number of transistors connected, a quick reading of the collector voltages (at the 2k resistors) will indicate best Vbe and beta matching within the group. After identifying the best collector current matches, confirm that their base resistors read the same too. Weed out any where both collectors and base voltages don't match. You can confirm matching at several different currents by varying the total current sent to all transistors.
Depending on how many transistors you have and can test at once you can either pre screen all for closest rough matches first or just weed out and replace the worst ones from the 10 or 20 being tested concurrently as you converge on the best matches within your group. It might be nice to use one of those plastic plug in prototype strips to hold a bunch of devices at once without soldering to the leads which will heat up the part.
You might wait until after getting a promising group of matches before heat sinking them together for final best match, to save time. The bad outliers are not likely to get better after being heat sunk, but you want the best matches that stay matched when held to the same temperature.
JR
PS: The VOM diode tester may be an easy way to prescreen devices but i wouldn't trust it for final matching.
and sometimes I think I need to read twice, think and repeat! 
