The Transit Bag for the MT45 is Engel P/N TBAG45 and is available on their website for $156.98.
The handles are Engel P/N 3233 010 00X9 http://www.engelcoolers.com/media/wysiwyg/parts/MT35-45F.pdf
Have you tried contacting Engel's U.S. distributor to obtain the handles?
Engel
900 Jupiter Park Drive
Jupiter, FL 33458
561-743-7419
http://www.engelcoolers.com/