Well made custom ICC profiles will always make your prints look their best. Check where you got your ink from, they may offer a generic one for your printer that will help.Recently I converted a new EPSON L120 to use sublimation ink.
Printed some test papers and played with the heat press till I got some good results.
Wanted to know : If I use a custom ICC will my prints get more vibrant colors ?
Test prints were done using the sRBG profile
See attachments from my tests.
The tee is 51% cotton 49% polyester, light grey ( Used un-cotton paper just to see what happens ).
Not used any powder or added polymer adhesive, just regular sub paper and heat pressed on different time&heat settings.
Artwork : [media]https://i.imgur.com/42rlLjh.png[/media]
Printed Sub : [media]https://i.imgur.com/QA41902.jpg[/media]
( The elements near the artwork are just previous heat press tests )
Also 100% polyester substrate will have much better color.
Some of your print (on the shirt you described) will wash out in the laundry.
Your colors dont look bad for no profile and the wrong fabric. Dye sub is really for polyester or mostly polyester clothes. Cotton doesn't really work for it without using other products.