You redirect stats from pg_class and pg_statistics to a local hash table. This is pretty hairy :( I guess you'd also need to handle pg_statistic_ext and ext_data. pg_stats doesn't work, since the data isn't in pg_statistic - it'd need to look at pg_get_gtt_statistics.
Without this, the GTT will be terribly slow like current temporary tables with a lot of problems with bloating of pg_class, pg_attribute and pg_depend tables.