I scrounged thru the fat folder on engorgement.  Best Ref is ABM protocol #20 from 2016 and available on their website.  These protocols are revised every 5 years and i'm sure if anything radical came up (like no ice) they would let us know.
A comparison of cabbage leaves vs. Hot and Cold Compresses in the treatment  of breast EngorgementArora, Smriti, Indian Journal of Community Medicine, 33 (2); 2008.  The conclusion cool cabbage leaves, vs alternating hot and cold compresses (more effective.
Treatments for breast engorgement during lactation (Cochrane Review) 2016 by Mangesi, L.   Basically found little research with multiple results.
ILCA's Inside Track for breastfeeding mothers: Overly full Breasts (Engorgement)  Hand out (2014)  Warm application for a few minutes prior to nursing , pumping or hand expression.  AND Reverse Pressure Softening so  baby can latch.  Free download jhl.sagepub.com

Mothers value and utilize early out patient education on breast massage and hand expression in their self management of engorgement. A. Witt, M. Bolman, Kredit, S. Breastfeeding Medicine 11(9); 016  (personally I think this ed should take place in prenatal classes with a repeat during their hospitalization BEFORE discharge)The Inside Track mentioned above is a great handout.
Breastfeedingonline.com/rps.shtml has a great handout from Jean Cotterman on reverse pressure softening.
Another hand out is Taking Care of sore nipples and breast engorgement  (In English and Vietnamese) .  They recommend warm pre feeding and cold between feedings for comfort.  
It is supported by State of California, Dept of Health Services, WIC Branch and the Santa Clara County WIC Program.  Au is listed as Nguyen, K-P, Mai, CT and the Santa Clara Valley Breastfeeding Task Force. (no date)

The Milk Mob has a handout (2016) Help, My Breasts are Swollen & Engorged! What Can I Do to Feel Better?  They recommend heat, massage & reverse pressure softening before nursing and cold packs after nursing.  Specify how to use cold packs for 15-20 min and not damage breast skin by wrapping cold packs with cloth.
Newer articles seem to emphasize massage and RPS more often.  We have  a lot of earlier articles(62) consistently saying cold..I don't have a clue where the new ideas are coming from.  I can't say I've ever heard a mom saying it decreased the milk supply, just the swelling.  Milk supply comes in , usually with engorgement and then as baby and mom get into a routine early oversupply calms down to what the baby takes out
WHERE IS "THEIR" RESEARCH TO SUPPORT WHAT "THEY" ARE SAYING???


             ***********************************************

Archives: http://community.lsoft.com/archives/LACTNET.html
To reach list owners: [log in to unmask]
Mail all list management commands to: [log in to unmask]
COMMANDS:
1. To temporarily stop your subscription write in the body of an email: set lactnet nomail
2. To start it again: set lactnet mail
3. To unsubscribe: unsubscribe lactnet
4. To get a comprehensive list of rules and directions: get lactnet welcome