What are some atypical examples of positive transcriptional cooperativity?
Positive co-operativity without feedback from the downstream genes:

I guess Polycomb/Trithorax complexes will fit this criterion nicely.

Polycomb group (PcG) represses Hox and other differentiation related genes (such as neurogenin) while Trithorax (TrxG) group promotes their expression. They are not like usual transcription factors that bind to promoters and recruit/exclude RNA-polymerase; they bind at regions called Polycomb Response Elements/Trithorax Response Elements and mediate epigenetic regulation of nearby genes by histone modifications (primarily methylation). 

PcG froms two main complexes PRC1 (Polycomb Repressive Complex-1) and PRC2. Different components of the complex have different molecular functions. For e.g SuZ has a Zinc finger domain and can bind to DNA/RNA, Ezh has histone methyltransferase activity etc.

This is an old review but is still quite informative.