search_api cron broken

Hi! After searching this site for all related issues I could find and following all of the recommendations (at least the ones I could understand), I still have a problem with my search_api cron. I have a commerce kickstart 2.x (drupal7) website that has been operating (mostly) smoothly for 1.5 years, hosted by Pantheon and indexed with IndexDepot. The problem findings are as follows:

1. All of a sudden I can't index the site. It gets stuck at the "Initializing" step. It gives me the following error message:

An AJAX HTTP error occurred. HTTP Result Code: 502 Debugging information follows. Path: /batch?render=overlay&id=4318&op=do StatusText: Internal server error. ResponseText: 502 Internal server error. #page {width: 416px; padding: 10px; margin: 200px auto; border: 1px solid grey; background-color: #DFDFDF;} body {background-color: #CCC; margin: auto; font-family: Helvetica, Ariel, sans-serif;} Page Could Not Be Loaded The request could not be completed due to a networking failure.

2. Log reports "Attempting to re-run cron while it is already running"
3. Watchdog reports:

[24-Mar-2016 18:53:43 America/Los_Angeles] PHP Fatal error: Uncaught exception 'PDOException' with message 'SQLSTATE[HY000]: General error: 2006 MySQL server has gone away' in /srv/bindings/320bdbe2c8c7462db64ed10f08017b5a/code/includes/database/database.inc:2171
Stack trace:
#0 /srv/bindings/320bdbe2c8c7462db64ed10f08017b5a/code/includes/database/database.inc(2171): PDOStatement->execute(Array)
#1 /srv/bindings/320bdbe2c8c7462db64ed10f08017b5a/code/includes/database/database.inc(683): DatabaseStatementBase->execute(Array, Array)
#2 /srv/bindings/320bdbe2c8c7462db64ed10f08017b5a/code/includes/database/database.inc(2350): DatabaseConnection->query('SELECT expire, ...', Array, Array)
#3 /srv/bindings/320bdbe2c8c7462db64ed10f08017b5a/code/includes/lock.inc(167): db_query('SELECT expire, ...', Array)
#4 /srv/bindings/320bdbe2c8c7462db64ed10f08017b5a/code/includes/lock.inc(146): lock_may_be_available('schema:runtime:...')
#5 /srv/bindings/320bdbe2c8c7462db64ed10f08017b5a/code/includes/bootstrap.inc(433): lock_acquire('schema:runtime:...')
#6 /srv/bindings/320bdbe2c8c7462db in /srv/bindings/320bdbe2c8c7462db64ed10f08017b5a/code/includes/database/database.inc on line 2171

4. cron_debug module told me all crons ran successfully except search_api and the error message says "Cron presumably failed while running the cron hook search_api_cron() in the module search_api"
5. semiclean module reports that cron is not running
6. cron is supposed to timeout after 3 minutes, but it actually runs for almost 30 minutes (all the while posting a 504 error to site visitors)
7. After doing "drush vdel cron_last" there is no change to the above problem description (and for some reason it doesn't find any cron_semaphore table)
8. Using phpmyadmin and the sql query provided on drupal.og "solving cron problems" it does not seem to be a content issue, as all my active nodes were noted as needing re-indexing (plus we haven't changed anything about the product categories)
9. My search_api_task table is only ~4000 items long (I have ~7000 active products)

If I have missed a related issue I apologize, as I know you have better things to do. I have spent >30 hours trying to solve this problem and I'm stuck (just like my cron is). I am not a developer, just a retail business owner, so if you could give me the "for dummies" instructions that would be great.