Assign record to different type without conversion function in VHDL
To answer the question directly:
Is it possible to assign a record to a different type without conversion function in VHDL?
No, you will need to write a custom conversion function, or split the assignment out manually as per the comment by @user8352. As you say, this looks messy and is error prone, so a custom conversion function (probably inside a package) is the way to go.