Can the Ward Clerk login to LCR and verify that you are both listed in the calling and set apart? I don't know for certain that a set apart is required for access, but it seems to not be a problem for those who have. Right now LCR is kind of the authority for callings (I don't think MLS is allowed to edit callings anymore), so it might be that the Ward Clerk will need to update that calling online. Also, when he's checking online, it'll be important for him to verify that you weren't accidentally assigned to a custom calling (it'll have an * next to it, in the callings list). Only official callings are mapped to LCR access, yours should read as "Ward Assistant Clerk--Membership"
If the above was done, the incorrect display in LDS Tools could also be due to not having synced it. It can get out of date pretty easily.
We recently had a stake clerk adjustment that took about 4 days for the new clerk to gain access to everything, so two weeks should definitely be more than enough time to take effect (usually it's within a few hours). Sorry if I've repeated anything you've already tried, just trying to cover all the bases
