Cron run exceeded the time limit and was aborted + How to change max_exec_time if not access on php.ini
Seeing as you don't have access to anything that allows you to change the max execution time (and I would imagine if you find a workaround that it won't work if your server is this locked down) I see a couple of options.

1:  Utilise the Batch API as I mentioned in my comment (Batch API docs are here)

2: Check out Elysia Cron to split your cron tasks up into smaller, more manageable chunks.


  Elysia Cron extends Drupal standard cron, allowing a fine grain
  control over each task and several ways to add custom cron jobs to
  your site.