It seems the most straightforward way to do this is to just use a pickup machine and play with the gain parameter. I’ve done pretty much what you are talking about running my acoustic strings into the OT, looping them with a slight reduction of the gain, so that the pickup acts as a really slow delay, great overdubs but the oldest layers fading out gradually.

Edit: I should add that the “delay time” of your pickup machine loop is however long you decide based on when you start playback of the loop. Just make sure you have RLEN set to Max (unless you want to use a set step length) and use Dynamic Recorders.