Now, to check if you have issues with the stick coils.
(I don't know how mechanically inclined you are, sorry if this is already obvious to you.
The ignition coils ("stick coils") are INSIDE the valve covers, at ends of ignition wires, plugged onto the spark plugs. There are 2 plugs per cylinder, but based on the severity of the problem, I'd blame the main plugs - facing you, not the secondary plugs underneath cylinder heads.
Below is a picture from a spark-plug changing thread
at r1200gs.info - this shows how to pop off the cover to access the stick coils.
Get the cover off and feel with your finger if the coils are solidly seated.
You can try pulling out the stick coil if unsure. You should have a little plastic coil-removal tool in your kit, otherwise use a screwdriver as shown here. Be careful, go easy to avoid ripping up the coil head (I'd use 2 screwdrivers) and make sure to protect the valve cover with something soft, like the cloth shown here.
Or, use the wire method:
If the coils are seated, one of them could still be faulty. One method to check that is to disconnect one of the coils wires, tape up the end and start the bike. If it is much worse, you disconnected a working coil. If there is no change in behavior, you disconnected a coil that was not working.
Here is a picture from JVB's post
that shows the top of stick coil and the connector that needs to be undone to disconnect the wire. There is a little tab on the connection - pry it up slightly with a small screwdriver and then pull out the connector away from the coil.
I hope this helps in your troubleshooting. Since you believe that the problem started with the service, I'd look at things that were disturbed during the work (like the throttle cables or the coil sticks), before worrying about actual component failures