Well how large is this battle supposed to be? You seem to want the Goblins and Dwarves to be evenly matched, which eliminates my first and last examples, but I don't see how the 'leader' and 'hidden elite' examples fail to mesh with what little information was provided. I assume you have more to the encounter in mind that you didn't put up for simplicity's sake, which puts me at a disadvantage.
I also want to ask how you'd deal with a large scale battle in 3E. Would you compartmentalize it, having the PCs fight in one small skirmish of the overall war, with reinforcements constantly coming in from both sides, at a time, having them secure the lines area by area? If so, replacing just one regular NPC on either side with an equal XP value number of minions could be used to add drama to the situation. If the PCs aren't told what's a minion and what's not, seeing half again the normal number of Goblins could create good dramatic tension, while having half again the number of Dwarves could add dramatic impact when the line crumbles from the minion's deaths. You don't necessarily need to use them in massive numbers, remember, just swelling an enemy party enough for dramatic tension is enough to add something different to an encounter.
If you'd do it all the math at once with a battle consisting of more than 20 NPCs and PCs, I feel bad for you, I really do. Minions might help speed things up a little, but using them in smaller numbers as I suggested above, as you've said, just doesn't solve your problem. It's a specific design choice, and I will admit that minions just don't fit into every encounter, in the same way Elites and Solos don't. I for one will use them in small numbers or not at all most of the time, only putting them out in large numbers every so often so that kind of encounter doesn't begin to feel underwhelming.
Final question before I head off for the night: what exactly is your problem with minions? You've been somewhat vague, only talking about unspecified problems. I assume it comes from the view that any one of these Dwarves or Goblins should be the equal, or at least close to, the PCs in terms of strength. Is this correct? Especially at lower levels, you want the PCs to feel that they're a part of the world, not somehow better than a large number of its inhabitants. This is you specifically deciding minions don't fit into the situation, which is fine, but shouldn't be a deal breaker. After all, in another ten levels, what's wrong with the Goblin threat having grown larger in the PC's absence, but given their new level of power, Goblins are now merely level appropriate minions with much greater numbers than before?