I'm delighted that this game as a very Fire Emblem-esque leveling system, but I'm very curious as to what character growth rates actually are. Does anyone have that information?

What do you mean, exactly?

Characters level up by being used in combat.

For people who dont know, Fire-Emblem used a similiar random system as Kamidori, im not sure if its the same, but FE System is like this:*easy example*
Hero A
Strength growth: 20%
Speed growth: 70%

Now he gets from lvl 1 to 2, theres a 20% chance he will get one strength point and a 70% chance he will get one speed growth.
If he doesnt get any stat up, the % gets "saved", so from lvl 2 to 3 he will have 40% chance for one str point, and 100% for one speed aswell as 40% for a second point in speed. When he got a stat point it resets and stars from 20/70% again, so he basicly asks if the growth rates of the kamidori char's are known.

It's random.

Seems he's right and there are two different patterns for each character.
But they don't appear at random, just even/uneven turns. if you save, lvlup and get bad results, reload, make one turn (possibly standby) and you'll get another result.

Just for clarification, only the newer FE's(FE11 onwards. ... Which is basically the DS ones only so far....) have what's known there as dynamic growth rates where 10% of the growth is theorized to be added to the next level.

At any rate, the game's stat caps are relatively low compared to the number of levels you can obtain before class changes, most of your units will have no trouble at all capping every stat until you reach the New game + Classes(i.e level 50 and above) at which point, the stat caps are removed entirely(everyone has 100 for their max stats).

For the record, starting over at level 1 is not recommended even though you get an item that increases your growth rate at the very end of the first playthrough. 3 factors make this unfeasible. Low class caps until level 50(which is hard to attain on first playthrough anyway) means the primary benefit is towards your hp/sp/fp. NG+ quests assume you are approaching level 50. On hard games, enemy levels are averaged between the top... 8 members in your group. Given that the mascot characters are very easy to recruit, you may find your main team severely underleveled.'m talking level 17 to 20 versus level 40+ enemy mobs.) Lastly, there are reincarnation item/accessories that allow you to restart from level 1 anyway. You might as well save the regrinding for when you reincarnate to get higher stats.

Oh and there's definately more than even and uneven turns involved, perhaps it's more noticeable with the 1.5 growth ring on or a larger sample of turns was needed but I've seen more than 2 patterns of growth.

Tldr? It doesn't matter for first playthrough. You're grinding in second playthrough anyway.