As noted in the question itself, works in respect of which copyright has been restored in the United States receive protection automatically without the need for compliance with any formality. 17 U.S.C. § 104A(a)(1)(A). The European Communities and their Member States are incorrect, however, that enforcement of this protection generally requires compliance with the "notice of intent to enforce" procedures set out in the law. Service of a notice of intent to enforce is required only with respect to a claim against a person who used the work in certain ways prior to restoration-a "reliance party", as defined in the Copyright Act (§104(h)(4)) and only if the copyright owner has not filed such a notice with the Copyright Office within the two-year period set out in the Act (§104A(d)(2)(A)). As to all other users of restored works - the vast majority of infringement claims - the copyright owner can proceed with an infringement case in the same manner and to the same extent as for a newly created work. See §104A(d)(1) (Enforcement of Copyright in Restored Works in the Absence of a Reliance Party).
Accordingly, the "notice of intent to enforce" procedures apply only in a narrow category of circumstances. As explained by the United States in response to question 5 from the European Communities and their Member States in connection with the July 1996 TRIPS Council Review of Copyright Legislation, this approach to restoration of works in the public domain is fully consistent with the requirements of Berne Article 18 and Articles 9 and 14.6 of the TRIPS Agreement, as a reasonable and limited "condition of application" of the principle of retroactive protection, to deal with the special situation of those who have in the past invested in the use of material then in the public domain.
In response to the request for a description in the second paragraph of the question, the conditions in which infringement actions may be brought with respect to restored works, the evidence available to the copyright owner, and the sanctions that may be imposed on infringers, are all identical to those involved with respect to any other copyrighted work.
Finally, the United States disagrees with the question's characterization of the notice procedure as "long, complex and costly". The procedure could not be simpler or more inexpensive. It merely entails sending a short statement on a piece of paper, in no particular format, signed by the copyright owner. The statement must set out the basic facts necessary to indicate a claim: the work's title (including a translation or alternative titles), the address and telephone number of the copyright owner, the use to which the copyright owner objects, and, in the case of a derivative work based on the restored work, an identification of that derivative work. While service of a notice does necessitate locating the reliance party in the United States, this is no more difficult than identifying any infringer located in another country.