I have never seen a picture from a minimig with a 2.04 bootscreen.
But the minimigtg68 can boot all versions of kickstartrom.

Now I found a little but important difference in the 68sec000 and the
TG68 IP Core.

The tg68 is a 68000 Clone. But the 68sec000 insn't a 68000 and isn't
a 68010. That is the Problem.

The Move from SR is priviligated in the 68sec000. Kick >= 2.04 use
this Instruction to check the CPU Type.
For the kick 2.04 is the 68sec000 a 68010. But the 68sec000 has the
exception stack frames from the 68000. That can't work without a
patch.

But the TG68 use the Move from sr in user state and use also the
68000 exception stack frames. That works fine.

I think the TG68 IP Core is the better choose for the minimig!

Viele Grüße
TobiFlex - the creator of the TG68 Core ;-)