This is confusing to me, what is taking up your time?
The way I see it people choose what they want to spend their time doing. Sometimes they choose research, sometimes they choose game playing, sometimes they choose reading Hacker News :-) but there is generally enough time for folks to do what they want to do.
Research is especially easy if you know what you want to research. But it's not a simple matter of "Hey I'm in research, lets blue sky something!" People in research have some passion that they are following, like parsers, or graph theory, or AI, or network coherence, or something. Some area where they have lots of questions and no answers.
Keep a notebook. One for each topic if you want, they can be the cheap composition ones that go on sale during 'back to school week' or really nice lab notebooks. But they are like pitons and rope to a climber, they anchor where you have been and where you are going. Write the questions you investigating into the first few pages after the index. Start writing down what you know, what you can prove, and what you don't know. Invent experiments or ways to discover the answers to the questions you don't know.
I've got a notebook with a couple hundred pages devoted to making carbon nanotubes. I know lots of ways you can't make them and several ways you can. Sometimes you can scrounge equipment for stuff, sometimes you have to invent (did you know that you could use a bottle of propane and a chunk of copper pipe as a way to do vapor deposition of carbon? You can! And if that copper tube rolls off the stand onto your wooden deck when its hot it leaves a big black mark? :-)
"Research" doesn't need a government funded lab, it needs good laboratory technique. Careful note taking, documentation, exposition and analysis. Software research is even easier these days because of how cheap computers have become.
In general, having a job doesn't prevent you from asking questions or doing experiments (aka "research") but if you're tired after working all day and just don't want to think any more, that is a different problem. Some folks I know get under demanding jobs just so they can do it easily without straining too hard during the 'day.'
One of the things I did as a kid that drove my Mom nuts was read every scientist biography I could, I tried to re-create their experiments because anything an adult could build in the 1800's I figured I could build as a kid in the 1900's. But what it really taught me was how these people pursued the questions they had.
Bottom line, "money and free time" isn't an excuse, its a rationalization. Why are you denying yourself your own research?