I agree.
Give them:
- all the techs known by at least 3 race (2 if only two races remain).
- a 60% chance of getting a tech known by 2 race (1 if only two races remain).
- a 30% chance of getting a tech known by 1 race (ignore if only two races remain).
- a 10% chance of getting one tech more in each branch (once for each branch).
To give techs, work the tree upward and stop a soon as a tech fails in a branch.
This way:
- a new minor is at least on par with the middle races of the galaxy
- he is likely somewhat behind the second race (depending on how the techs are spread between races)
- he has a chance of getting free stuff that nobody other has (giving you a chance to trade with him and not making him worthless except as a spy

)
- he won't have all the techs that only two races share (or known to only one) (the 60% ensure that he'll miss some of them)
- he won't be able to work up very high in a tech branch known to only one or two races (the 60% ensure that he'll fail at some time working up in the branch)
Then, run an analysis of his tech situation : if he looks a little low, give him more ships/money to defend himself against greedy predators willing to seize a brand new class 15 planet. Hence, you also could end up with minors that come in not with a large tech knowledge, but with a large fleet, and which could pose different threats and problems.