I've been growing peonies for over 20 years in zone 7b-hot summers, mild winters with barely 400 chill hours-and yeah, those retail "bulbs" are often junk. Standard advice like "just plant 'em deep and wait" is lazy; it ignores how marginal chill screws bud set. On viability, I've ditched anything with more than 20% soft roots or fewer than 3 firm eyes-tracked it last year, and that threshold got me 85% survival vs. 40% for sketchier stock. No fancy ratios, but eye count beats root mass every time for predicting first-year stems.
Pre-plant, I skip long soaks; 4-6 hours in room-temp water with a pinch of H2O2 (0.2%) perks 'em up without leaching carbs. Tried kelp once-waste of time, no edge over plain. For rot, Bacillus subtilis dip post-trim works better than chemicals; zero impact on break, and it cut rot losses to under 10%.
Chilling post-purchase? Only if eyes aren't pushing-2 weeks at 4°C helped my late-spring Itoh divisions bloom year two, but risked mush on herbaceous ones. Direct plant deeper (6cm here) keeps crowns from frying, but log your soil temps; mine hit 28°C at 5cm last summer, tanking buds.
Itohs are champs in warm spots if established cool-85% flowered by year two vs. 50% herbaceous. For rescues, trim to firm tissue, dust with cinnamon (cheap bio-fungicide), and pot for a month; saved 60% of moldy crowns that way. Share your chill data-mine's all anecdotal, but I'd love metrics to refine this.