I accepted a patch from Andy Clement (up until recently, the SVN repo was closed for commits). It does make the initializer available in the field, but there is another problem that this uncovered.
When the field is a property (ie- it has no modifiers), then the field is created twice: once during the parse, and then once again because of the property. This is wrong. It looks like JDTClassNode.createPropertyNodeForMethodNode is being called on the getter method for that field and accidentally creating a second field with the same name.
I think I know how to fix now.