Their IT guy?? There are gazillions of people like me who have a blog, or some small project that has a small audience of tens to just a few thousand users. All these people now have to fork for SSL, or have to move everything to a different shared hosting that supports Let's Encrypt.
Your shared hosting service doesn't need to support Let's Encrypt, it just needs to allow you to upload a certificate. You can use https://gethttpsforfree.com/ to generate it.
The renewal is the same, follow the steps and you get a new cert. Keep the Account key and the CSR, so it's just a matter of copy-pasting. If they charge an installation fee again, you're probably better off paying for cert that lasts longer (not from Let's Encrypt) - you can get one that lasts three years for $15. Or just switch hosting providers :)
Right now, you can just put Cloudfront in between. It's free, and takes maybe 5 minutes to sign up and adjust your DNS entries.
Of course relying on a provider that might cancel the free plan at any time is not ideal, but worst case you just have to revert your DNS and it's done.
I assume you mean Cloudflare and not Cloudfront. While you could use Cloudfront, AFAIK there's no free option. (Aside from the usage you get as part of the AWS free but that is time-limited.)
It is, but it might work for your app, too – js/css/image caching at CF nodes helps a lot. Moreover, you can disable their cache/cdn features and use it only for SSL.
They even have multiple modes, the "Flexible" one works even with no changes at your server at all. It obviously makes the CF<->server transfer insecure, but your users would still get a "green lock", if that's what you're after.
