Last year I did exactly what you suggested with the six packs and all went perfectly well. In fact, I even started some in soil six packs and they transplanted fine too.
I personally like to start seeds in a damp paper towel then transplant to the six packs after they've germinated. 3 weeks for tomatoes is too long. they'll usually sprout in a matter of days. peppers, on the other hand, sometimes take up to two weeks.
I know a lot of people use rockwool, unfortunately only the people having bad results post about it, so it appears to be a difficult substrate to germinate in. I can't speak to it as what I mentioned above has always worked fine for me.
Anyone else?

Rock wool works fine for me, with chiles even. See below.

I had bad results when i started with rockwool. However, I now have a number of lettuce, peppers and even (finally) some tomato plants. Sprouting.

Now i'm FAR from an expert, but i'd like to share with you what I have learned of rockwool.

First of all, you HAVE to soak them in pH 5.5 water. Longer is probably better, but after an hour your definitely getting diminishing returns. I soak mine for about 20 minutes. Note these are the A-OK plugs from Grodan that don't need to be soaked a lot. Non starter cubes should be soaked longer.

Second, Don't use the hole that's there. It's too deep, and you can't get the seed to make good contact with the rockwool without damaging either the seed or the rockwool. Instead, turn the cube over, stick a screwdriver down to your desired depth, place the seed inside, then press lightly on the top so that the seed makes firm contact with the rockwool but DON'T SQUISH THE CUBE.

Third, once you've wet it, you don't really need to water rockwool if it's in one of those mini greenhouse dome thingies. It's vitally important you don't let rockwool sit in water. If you do, the water will wick up into the rockwool and it will be downright soggy.

This is what i'm now doing, and it works quite well. And the fact that it retains so much usable moisture is really handy! I soak em, and I haven't had to water my tomato seedlings since they were planted over two weeks ago. I do check them every day though. Mostly because checking my garden involves going downstairs.

i only start my seeds in rockwool and never had a problem.
i soak the cubes in water for a few hours then put two seeds in each cube and cover the cubes for humidity.

Starting hydroponics seeds with perlite or vermiculite can be a good choice because the porosity of these media allows for good drainage and oxygen availability. Rockwool is also a porous material, which makes it a good choice for seed germination. However, do not forget to soak the seeds prior to germinating them to make the seed coat become saturated with water so that they can easily break open.

I had trouble at first, but yes now I can do about anything in rock wool. @stevey's recommendations are perfect. An additional note would be to, just like soil, drop a couple of seeds in and pluck whichever one isn't doing as well after germination.

Aside from that I've also found that you can beat things up a bit and they'll work fine. I'm growing lettuce now, but want to do tomatoes/peppers in the fall/winter. Just for kicks I took an extra tomato seedling growing in soil, about an inch tall, ripped it out and dropped it in some hydroton. It's not getting much light due to an over-excited head of lettuce, but it's at 2 inches with 4 leaves after 3 days.