I have been just DCA on River and when it hits a certain point I withdraw to onchain address. If lightning channels rarely ever forced closed I'd open a channel swap out completely and stack slowly into that channel but sadly I have had a terrible time on lightning with force closes so stacking via lightning for me is a no go. 

 I’ll explore it a bit more and let you know if I find a good way to do it via lightning. We must be early because it seems like there should be a ‘easy’ solution but I’m positive I’m missing nuance.