You have made the job a lot harder for yourself as to work the plastic has to be absolutely clean so you will have to get all of the putty out, scrape with a stanley knife blade or really sharp chisel.
Plastic will only bond to plastic so any dirt or left over putty will prevent it bonding .
final wash with acetone & a stainless steel brush ( must be stainless, not plain steel or brass ) will help .
Put a thin strip over the crack then a wider strip over it and a wider sill over the other two
Where the crack does not join together I V groove the crack, fill with round rod, still using the hot air gun, then patch over the rod .
Most 5 gallon chemical drums are HDPE and about the same thickness so make good practice materials.