Karabas, you are not alone in this situation. In fact, there are hundreds, possibly thousands, of foreign-trained engineers in the US with this predicament. The problem is usually with humanities and liberal arts requirements. This situation is usually not "news" because each person whom the state licensing authority declares to have inadequate education typically quietly "licks his wounds" and heads off to the nearest community college to take additional humanities and liberal arts classes to get over the hurdle. However, if it is true that you are INDEED deficient in design requirements, then your degree may really have problems.
ECEI is part of ABET and the reviewers will use only material that is known to ABET. Most times, the problem is not in the adequacy of the training but in the interpretation by US evaluators of what was learned in the foreign university. Unfortunately, most foreign universities don't do a good job of explaining their course contents in a way that would make US evaluation easier. That is probably why the contents, as listed by your university, did not adequately indicate that your courses on "tunnels, reinforced concrete bridges, steel bridges, road design, construction of roads, urban planning", etc. could indeed have qualified as design courses. My suggestion is that you find an established professor in a reputable US university, who is familiar with your university's civil engineering program, and who can vouch for the integrity of the contents of your design courses, to analyze what you have. Request that (s)he sends to ECEI an objective evaluation of your courses. If a good case is made, the evaluators are generally open to learn what they don't already know and can make revisions in their initial evaluations.
I suggest you read the following paper titled, "Need to Understand Foreign Education in Evaluating for P.E. Licensure" in the ASCE Journal of Professional Issues in Engineering Education and Practice, January 1996, pp. 26-30, as well as the discussion on this in the April 1997 issue, p. 91.