If it is greyed out, then you are already using the Cool VL Viewer method (outfit.xml) file and should not need to have/care about the Current Outfit..To make that option available, you will have first to check the "Use the COF in OpenSim grids" option in "Preferences" -> "Cool features" -> "Inventory".
Err... Are you telling me that you are using the "Current Outfit" folder to store outfits (or anything for that matter) ? You should
NOT store anything yourself into that folder (that is by the way hidden from the user by default in my viewer, and that would normally not accept items at all: you may only delete links from the COF in my viewer, but only as a last resort for corrupted/failed bakes in SL, when their AIS inventory back-end goes flaky, for example) ! It is used only by the viewer to store links to items your avatar is wearing, and in SL, by the server to bake your avatar from the list of those links.
The COF was introduced in v2+ viewers, after LL changed the way the list of worn items are stored (they used to be stored server-side and the list sent to the viewer for restoring the initial outfit on login, but LL removed that service from their sim servers when they allowed multiple attachments per joint, because the service was not designed for it, and so they needed another way to store the worn items list between viewer sessions: they opted for an inventory-based (non-user-actionable) folder, which also sometimes causes failures to restore the outfit, when the inventory fails to fully load or gets somehow corrupted.
Since I was not using the COF at all back in that time (pre-server-bakes), I developed a different, more reliable method to store the worn items list (in fact, at first, only the attachments list needed to be stored and worn wearables were still stored server-side, but this too changed latter on, when multiple layers per wearable type were implemented), using a xml file.
When LL introduced server bakes, they naturally used the COF to implement it, and I had (with much regret, rumbling and rambling), to implement COF support (from the ground up, to avoid LL's racy and intricate code) in my viewer... This said OpenSim servers do not rely at all on the COF, and so using it in OpenSim is totally optional (and only useful if you are using several different viewers or computers to log in with the same avatar).
This is indeed totally abnormal, and the sign something is amiss with your inventory as it is stored server-side...
Like I explained, you will have to restore manually your outfit the first time you relog, but the outfit should be properly preserved afterwards. This said, since you were already using the outfit.xml method, it should restore just fine. Which brings us to:
This is not what I understood from your initial report, and got NOTHING to do with inventory and outfit matters... You are simply experiencing network issues (slow loading: the attachments that "float" are just mesh attachments which LODs did not yet fully load; to see the mesh queue status, enable "Advanced" -> "HUD info" -> "Show mesh queue" which will display the queue numbers while meshes load at the bottom right corner of the window).
There are many reasons why this could happen, one of which is changes you would have made to the networking parameters. Since they are many, and therefore lead to a gazillion different combinations of them, I would recommend that you wipe out your viewer settings (~/.secondlife/user_settings/settings_coolvlviewer_12624.xml) or rename it, so to restart the viewer with a fresh (untouched) set of settings...