Personally, I would avoid changing SSL processes close to the expiry of your current certificate if uptime is a significant consideration[1]. If it's a toy or personal use server, then sure, learn a new experimental solution and save some money.

If you have problems with letencrypt.org, there are cheaper options for a domain validation certificate than $150. namecheap.com generally has competitive prices on various types of certs from various registrars. options and is pretty easy to use, startssl.com has free domain validation certs, but the experience can be a bit harrowing the first time around [make sure you keep a copy of everything in a safe place, you don't want to screw up the idiosyncratic process that startssl uses]).

On production servers, it's always better to use a tested process rather than winging it. This is doubly true when you have a hard deadline like a certificate expiration hanging over your head.

[1] in fact, I don't even like to let certs get close to expiry even when I'm not changing processes, since missing the deadline can cause so much unnecessary grief

edit: A bunch of little tweaks, nothing that changed the main thrust of the comment.