Finding a research group where I can work remotely?
It is actually of mutual interest, but really hard to find an opportunity. Although, you are offering your time for free, group leaders are reluctant to take this risk to leave their research somewhere that they do not have direct (everyday) control. Note that you should work on a research project currently funded at that research group. In other words, the group leader should complete that project in the corresponding timeframe. Thus, too conservative to put the project completion at risk in favor of having a researcher free of charge.

Sorry for this negative answer, but IMO (maybe others have better approaches), the only possibility is to directly contacting some research groups and negotiating about this possibility. Remember that the judgement will be merely based on your experience and potentials. Once again, IMO, the only chance is if the group leader can find your profession useful for a part of the project, which is not critically sensitive.

Conclusion: there is no system for this, you need to convince the group leader personally.

Note: Another solution can be finding an independent researcher like yourself for starting a personally funded research project, but I think this is not what you are looking for.