You're using an Adobe 1998 workspace, that's good.
You're using a custom ICC, that's also good!
Are you using the same settings (paper type and quality) in the Epson print driver as when you printed the test charts?
Are you using the same transfer paper as when you did the test charts?
What transfer paper are you using?
Do you get the same problem with blacks on every product you print (fabric and mugs for instance)?
Have you tried converting to Adobe 1998 instead of Asigning?
What rendering intent settings are you using?
Can you post screen shots of the PS print settings dialog box?
Please can you restore your initial post, and state what you did to fix your problem, as other people searching the forum in the future may have the same issue you had...
Using FlexiStarter 10 and a Liyu SC631e & a Silhouette Cameo cutter. 2x Ricoh SG3110dn printers and Adkins Auto Clam press. Using Sublijet-r from Sawgrass. ..And I have gotten my money's worth out of this forum - saved Hundreds by being a Premium Member <-- IF you like this post PLEASE add to my reputation by clicking the 'Star' below this post on the Left