The material pirateship.com has on Priority Mail flat rate "cubic" pricing is worth checking out.
pirateship.com offers insurance (via Shipsurance), but take careful note of their exclusions, including:
"Additionally, collectible coins, comic books, sports cards and similar that are being shipped to be graded and have their value established are excluded. Collectible coins, comic books, sports cards, and similar are not excluded if they have already been graded and have their value established or if they were sold under a paid, commercial invoice or have a recent appraisal." ( https://support.pirateship.com/en/articles/3222601-shipping-insurance-terms-and-conditions )