There is not a separate lottery process for newcomers. There is a petition process, but I doubt that would work at any of the schools you mentioned since they are in very high demand and will have a waiting list after the lottery. Also, being new to the area and not having even attempted to make a neighborhood school work is unlikely to sway the district to grant you special dispensation. ACCESS Academy has approximately 350 students in grades 1-8. The prerequisites for entry are a single 99th percentile score on math achievement, verbal achievement, or cognitive, plus "demonstrated need." What, exactly, demonstrated need actually means is nebulous and depends on the capricious whims of whomever is in charge of the selection process for a given year. You should absolutely not count on your sons being able to attend a non-neighborhood school for 2018. The only certainty you can possibly have is to move into the catchment area of the neighborhood school you want your sons to attend.
PPS has no district-wide TAG services. Outside of ACCESS, the district does nothing aside from testing and identifying kids to minimally comply with state law. ACCESS only exists because the district was sued many years ago. It was originally slated to expand to a first through twelfth grade program, but has never had any real support from the school district.
The prevailing opinion of those in charge seems to be that gifted education is somewhere between inequitable and racist and that gifted kids already get 95+% on all the standardized tests and PPS manages to graduate 93% of the TAG kids, so it's a waste to spend any time or effort doing anything extra for them when that won't make any real impact on their stats.
If you're concerned about your gifted kids being challenged in PPS, you're going to have to supplement their education outside of school. You could join the "Portland Highly Gifted" and "Portland TAG Parents" groups on Facebook and solicit more specific advice or search old posts. Lake Oswego, Beaverton, and Riverdale are all more TAG-friendly.
