diggy
You don’t need to get 1.15.x working on the new server. You just need to run a full dump of the existing database (it helps turning it offline, disabling email fetching, and disabling any cron/scheduled task beforehand to prevent data loss), import the dump into a database on the new server, setup the new v1.17.2 codebase (don’t run the installer just setup the code), copy over the old include/ost-config.php from the old server to the new include/ folder, and update this file with the new MySQL information. From there you should be able to visit the site, login, and run the upgrader.
Please note if you are currently running any plugins you must download and place the new builds of the plugins in the plugin directory on the new server first before upgrading. Please make sure the file ownership and permissions are set correctly so that the webserver can use them.
Cheers.