I don't get those big third-wave rushes, regardless of what I've been doing in terms of wealth production. Something I always do is to set the pop cap to 35 or so and raise it a touch when I want more bodies, and it may be this that limits the size of the first non-mandatory migration wave.
If you're stuck with a bunch of extra dwarves, put them on food / drink / bed / space production (this is always a safe bet) or in squads of three. Having a teacher and all is good, but diluting any current military force by turning one squad of three competent dwarves into three squads of mostly goblin fodder is bad.
Give your newbie military a helm and mail shirt / breastplate plus a pair of shields each and let them spar. The helm and torso protection are just in case they try any wrestling moves and end up skidding somebody's upper spine across the floor. Once you've got enough armour to cover them and they have enough shield skill (Proficient at the very least, Accomplished if you have time), armour them up and let them wrestle. Once they've gained some armour skill and aren't slower than a goblin while armoured, you can either give them a 'proper' weapon or let them wield a @copper shield@ in each hand. A heavy shield is a perfectly good substitute for a hammer.
The squads of three are to reduce the amount of catch-up demonstrations needed, while allowing for at least one sparring partner to be available to any one dwarf. Give your military waterskins, always -- drinking is a huge time sink, and waterskins make the process much quicker.