I have sawn basswood on my Woodmizer sawmill, wanted to try making basswood paddles. You might benefit from what I found. Even with a brand new , sharp blade, you get an unacceptable fuzzy board surface cutting basswood. Apparently basswood grain cuts with a lot of grain tear out rather than giving you a smooth cut board surface as with harder woods. The woodmizer cuts wood sooo smooth that you normally only have to sand board surfaces rather than plane in order to get a good surface finish . I experimented and modified my mill's forward speed thinking that a much slower cut might be necessary, with no descernable difference in board surface.
I would recommend that you consider having your sawyer cut your boards 5/4 ( 1.25 ") as this will give you ample thickness to be able to plane your boards down to an accurate finish thickness of 1", assuming that is your desired finish thickness prior to routing your cove and bead edges on your strips. If your desired finish board thickness prior to routing cove & bead is 3/4", then 1" rough cut boards should be fine. Plain sawn boards would be OK as most of your strips cut from them would turn out to be vertical grain ranging from approximately 45 degrees to 90 degrees.