A gbak archive is a snapshot of a database, including metadata, and when you restore you get an exact copy of the original database. There are no options to transliterate characters or, indeed, to change any column type.
There are at least 3 ways that character sets are applied in Firebird:
1. There is the default database character set. That is specified when you create the database and is used as the default character set when you define a text column. Firebird 3 has introduced an ALTER DATABASE DEFAULT CHARACTER SET statement that allows you to change this. However, changing does not affect any existing column.
2. There is the character set specified for each text column. The character set is normally the default character set when the column is defined, but a different character set can be given. It is possible to alter the data type of a column. I have never tested changing the character set and whether transliteration takes place if you do. It may work.
3. There is the connection character set specified when you connect to a database. This is specified by the lc_ctype parameter that you tried to use. It is only available when you connect to a database. It is not available with the services API. When you specify a connection character set, Firebird will transliterate text data into that character set when you read data from the database. When you write to the database it will transliterate from the connection character set into whatever character set was defined for the target column.
IBX should recognise the character set for text data and set the codepage appropriately for each string that you read from the database and, if necessary, transliterate outgoing strings from the string's codepage to the connection character set. Recall that AnsiStrings in FPC each have a codepage associated with them and IBX is designed to set this correctly on read and to respect it on write, including using CP_NONE for character set OCTETS.
As a rule of thumb, unless you have a good reason not to, just use UTF8 everywhere including the lc_ctype.