Currently, my website is hosted by Site5 Web Hosting. It's coming up for renewal in a few months, and I'm looking to change to another company. My main problem with Site5 is that they want a lot more money for secure hosting (https), and they don't allow the use of outside certificate authorities such as LetsEncrypt. Any recommendations?

I can't speak directly to your specific issues, but I have used Ionos by 1&1 for years with no hassles or problems. Tech support has been very good when needed and they seem to be reasonably priced.

I'm webmaster for an RV Club that recently came up against the same renewal constraints you seem to be facing.....I did a search for suitable alternative hosting services and interserver.net was my choice. They did the migration for me, they provided https at no additional cost, their servers are all up on SSD's with really fast responsiveness, and their prices are FIXED so as not to balloon on renewal like most other services. It worked for my needs.....

Thanks for the suggestions. I've checked out both Ionos and Interserver. Both appear to be considerably less expensive than what I have now. Another person also recommended Ionos to me. However, it appears that for what I need, Interserver may be the best deal. I'm also looking at Dreamhost, which has a plan that's priced similar to Interserver's low end plan. Devil's in the details though.