Hey Brian
Interesting question and situation... here's my two-cents.
First I'd suggest going with Information Systems training to understand the relationship of programming to system development. Programming is the implementation of a system, and while it is important and perhaps fundamental, it does exist in an IT ecosystem.
A web page exists in a vast eco-system of collaborating software and hardware, and getting bogged down in the detail of programming (algorithms) may make it difficult to see the wood from the trees. You could get bogged down in the detail rather than seeing the big picture, which is especially important for a consultant.
Consultants can also piece systems together from existing components, and utilise existing software and services to compose a solution or design and implement (program) a bespoke one.
If you're interested in just learning one way to make web-pages then I'd follow through an online course at places like Pluralsight or Lynda.com. These are low-cost and easier to follow than academic courses, however are usually very narrowly focused on a single technology.
Full-stack typically refers to the ability to develop the front-end (user interface), business logic (rules) and persistence (database) layers of a single application.
Best of luck, I hope this helps you.
Kind regards
Michael Smale