First, understand that 4 hours a week is a lot. That is 26 days a year. That's 5 weeks worth of time. You probably don't really need that much. So don't feel bad that you don't get to it every week.
Second, goals like "spend 4 hours a week on research" are really hard to meet. Instead, work on having goals that are crisper. For example "move to the new version of [tool we use] within [x weeks] of release" or "never be more than [x releases] behind the latest on [library we use]" are simpler to measure, and carry their benefit right in the goal statement so everyone knows why you might need to do that. You can also have "try one new tool or library every month" and other slightly more open goals.
Third, a goal ignored is time not spent. I presume you're doing something at least semi-agile so every two weeks or so there's some sort of meeting, either looking back over what's just been done or looking ahead and deciding what to do. As part of those meetings, you can checkpoint against the goals. What's been released or announced? Are you using the latest version? If not, who will be getting you there now? What tool or library is each person going to try this month? How did things go trying whatever you each tried last month?
These checkpoints that already exist may provide all the structure you need, but if not, you can add a Lunch-and-Learn or similar peer-to-peer presentation. For example, if Jo tries out the new library and it's just not ready at all, a 20 minute presentation showing how, despite the buzz and hype when it was announced, it has nothing to handle [something important to your team] will let everyone know they're not missing an opportunity by not moving to that library. Then if Sue has been experimenting with a new technique and getting great results, a 20 minute presentation to at least show off the results (and perhaps start to teach the technique) will encourage everyone to learn it. The usual bribe for the lunch-and-learn is that the company orders pizza or some other hot food.
If after 6 months of crisper goals, including these goals in planning and retrospective meetings, and holding peer-to-peer presentations, people are still not learning new things and you feel that you are missing some important innovations as a result, it will be time to spend money. Pluralsight subscriptions for everyone, and encourage them to use the offline viewers during their commutes. Start sending people to conferences - it punches a one-week hole in the schedule and ensures lots of opportunities to learn new things. Hire another person and lower everyone's billable hour target a little. The cost for these things should be justifiable by the gap between developer's knowledge and what they could have learned by now.