So the whole issue is based on the ability of SH to choose their IDs? Let their ID be their number in the SH sequence. So the very first SH has ID=1, the one who registers after him ID=2 and so on. Their order for signing TBs is determined by a chosen good pseudorandom number generator in [1..number of SHs at the moment], initialized with seed value of 0 at the very first TB.
Not good? Please provide an algorithm to gain significant control over your position in TB signing queue with that (good luck). We can test it right away, I'll write the program SHs have very limited control over their ID now, they can just wait until the number grows to their desired position, or fill the IDs by creating a lot of SHs, which is supposed to be costly, and your resources are limited.

I skipped the rest because it was all based on this.