Edit: crossed post with Sam. Yes, a lot of the camera plates are model specific as well as being non reversible. I have also seen some slim-line long Arca rails that are one sided, but it's obvious when you look at them. The PhotoProShop I linked below is based in Germany I think
Sounds to me like you need an L-bracket - sorts out vertical shooting perfectly. Mine's a Markins
https://www.photoproshop.com/product_info.php/products_id/1004?osCsid=uji00cqqqhsm4rn2t0cifj9cv0 but there are plenty of others - Kirk, Really Right Stuff etc.
But to answer your question, yes (almost) all Arca-style rails and plates are reversible. Some have grippy bits on one side, usually the camera plates, whereas the lens plates tend to be bare metal, but you can flip them.
The usual problem is that the recesses for the mounting bolt heads are only on one side, but you can do anything with a pile of AS stuff, it's like Mecano, though I agree messing with tools it not practical in the field. I tend to go out pre-prepared and TBH if I did a lot of long lens work I'd get a custom gimbal for sure - and a nice long prime to go with it would be a good idea too

It's just that I saw that really cheap Feisol pan base and guessed, correctly, that it would be high quality and could be made to do other things with a couple of other cheap bits.
You would also benefit from configuring the balancing clamp arrangement I showed above, for your 16-35 lens which will be front heavy in either configuration, not having a lens collar. All you need is a 100mm rail (one in the pic is 140mm) and a spare clamp. The ability to slide the camera backwards, and sideways on the L-bracket, allows you to achieve perfect balance at all times and so there is much lower tension on the ball. Easier, more accurate, etc etc - really nice to use.
A quality ball head is always a good plan. Benro are high quality and cheap(er), with a 44mm-plus ball - J-2 or 3, B-2 or 3. Recommended supplier
http://stores.ebay.com/DCs-Photogra...Q2ec0Q2em14?_trksid=p4634.c0.m14.l1513&_pgn=1
HTH