Developer story for SharePoint-hosted apps?

My take is you are a bit stuck in the middle by the sounds of it. I would completely agree that SPFX is the best route to go for all SP development now but in your case you are left with some decisions. The hosted app model was a flop to most developers. If stuck with 2013 for a while - I would either go with JS embedding on the pages (Script part) or if you need even more power you can still use Server side web parts. At least the JS code would port forward a bit better later on - keep an eye on trying to structure it as close to the SPFX model as possible. 

I might get blasted a bit for Server side web part suggestions but depending on the needs these are generally easy / quick to create with max power in 2013. I wouldnt waste a year on development but for quick hit areas of your site you might consider it.