Uploaded images are saving to the server's temp folder and throwing 500 errors
Crappy shared web hosting?


That would be my guess. It seems imprudent to be developing a site on the same host as a live site, it has to share the (probably already stretched) resources available on a shared host and there isn't enough juice to run everything.

Solution? Get a $5 VPS, and see how it runs there. In my experience a properly configured $5 VPS will out-perform shared / managed hosting costing 5x the price. Most VPS can be billed by the hour/minute, so if you don't like it just cancel and you'll be charged only a few pennies.

Personally, I would recommend Linode + Serverpilot.

Both services can be cancelled without notice, so there's really no tie-in or big gamble.