I would also then reduce my oil cut-in. Maybe to the 150 range. If the diff is then set to 30 so cut out is 180, that should give lots of hot water to your baseboards. (Assuming baseboards?). Or 155 with 25 diff. 160 water vs. 180 water in the rads will just lead to the water circulating longer - should still heat your home. Might struggle recovering but should do the job. Unless your baseboard is undersized. Doing all that should cut your wood & oil consumption.
My father has an older Kerr that has tubes - I'm pretty sure it would benefit from storage. Biasi has decent heat exchange, I think. Not sure of others - but tubes or multi pass heat exchanging (while being easy to clean) are key, and should be able to utilize storage.
Well its definitely something i can experiment with....costs nothing.