Do I have to learn CUDA/OpenCL — which seems a daunting task to me — or is there a simpler way?
You do NOT have to learn CUDA or OpenCL. You can use libraries or compilers. GPU libraries tend to give better performance than GPU compilers (e.g. OpenACC) and tend to be able to handle more algorithms. That is because compilers are simply not smart enough to do things as well as expert programmers who meticulously hand-tune kernels and put them in libraries. Any number of libraries are available. There are many poorly supported libraries out there, so you may have to search around to find good ones. I suggest one below.
What, currently, is the most painless way to start playing with GPU programming? Surely there must a be a 'relatively painless' way out there, with which one can begin to learn how to harness the GPU?"
My colleagues and I at AccelerEyes have dedicated the last 6 years of our lives to trying to help people find exactly what you're looking for - "a relatively painless" way to harness the GPU. The result is our ArrayFire library for CUDA or OpenCL. I know it's uncool to toot one's horn, but the GPU computing community is small enough that people know each other and we're all working together to build out the ecosystem. There are many different contributions to GPU computing by many different groups. Our group's specialty in the ecosystem has always been the "relatively painless" contribution coupled with great performance. The reason people like our stuff is because we do nothing but work on squeezing out the most performance possible. Then we wrap up those kernels into convenient library calls that can be plugged in like math functions to your code with much less burden than writing the CUDA or OpenCL from scratch.
Happy to answer any further questions you may have about specific libraries, compilers, or GPU programming approaches. We eat, drink, and breathe everything CUDA/OpenCL.
BTW, we also encourage learning expert CUDA/OpenCL development. It is tough, no doubt about that. It is time-consuming and for many developers is not worth the added development complexity and lengthened development time. It sounds like you are probably in the boat of not caring about becoming an expert in low-level details, rather just wanting to get better performance to achieve a goal and be done with it. Is that correct?
Perhaps a Visual Programming Language or 'VPL' that lets you connect boxes/nodes and access the GPU very simply?
Labview does not have good support for GPUs. Many ArrayFire users are building custom Labview blocks so that they can program the GPUs more simply. I can connect you to some of those users if you wish (just shoot me a note to firstname.lastname@example.org).
I'm unaware of another graphical box/nodes package that supports GPUs.
While I'm at it, I know this post is going to be read by many expert CUDA/OpenCL developers out there. If you're interested in writing CUDA/OpenCL code daily, we're hiring (see my email above)