I bet most of those client websites would run just fine with Dokku. It's not ideal, but it'd probably reduce your costs at least. (Speaking as ex-herokai here, from what I've seen render.io seems to have the closest hosted experience, and unlike many of the other commenters in this thread I'm allergic to google cloud and would strongly recommend against GAE :) )
Thanks you, nameless912. I've been leaning towards Render, so cheers for the info. Will take a look into Dukku, but feel it's probably going back a step for my purposes as it'll involve managing a server (or set of servers).
It will, but the upkeep is extremely low. It takes roughly 15 minutes to set up a DigitalOcean box with Dokku (I think they can even install it automatically for you if you set up a cloud-init script). What I'd honestly do if I was managing a LOT of sites is write a tiny bit of terraform or something to stand up all those sites, and then delete and recreate all of the servers on like a quarterly basis so they all get patched. Slightly more upkeep, but an 8gig/4CPU DO box costs like 48 bucks a month, which is a hell of a lot better than Heroku at that price point.