There is a very good community of K owners in Europe.
I use a K100RT just now and have a K100LT. I don't go K1100 because too much weight for me.
The K100RT is 1984 and in 3 years has just put its 5th set of tyres on it and I get 10-12,000 MILES a set. In that time it has never let me down. I happily take it to Europe and have also done cross Europe runs in 20 year old cars. Every time I have been broken down it has been cars under 5 years old, never older ones. My son gets breakdowns on much newer bikes and cars.
From my own experience around here you have got some very good advice. I would never take a newish motor for a long trip.
Inside my tragkorb lids are stickers for Motorworks and Motobins, with phone numbers and web addresses. Sorted and you will get parts sent anywhere in next to no time. If you want even simpler you can also use an Amazon/eBay/PayPal account that you have set up so you can still get stuff if you lose your wallet!. Just set them up on a different credit card not travelling with you.
Clutch cable: put in a brand new one but use the genuine BMW one and not a pattern. At same time replace the nipple AND the sleeve that goes round the nipple. Then check the lever because it wears where the nipple sits and creates a ridge that stops the nipple rotating fully......and so it pulls the cable at an angle...SNAP. Lube only the nipple regularly. NOT the cable. Then throw the old nipple in somewhere safe. Snap a cable, spare cable is great but that's when you discover the nipple went too and that it doesn't come with the cable......
Throttle cable, same but also clean and lube up the chain mechanism......
Somewhere tucked away you need......spare clutch lever, front brake lever and spare gear lever. Why? Some fekr may knock the bike over and snap them. I have had it happen twice. And, take the old ones off and clean the splines/pivots and grease them up...so you know they will come off when you are away if they get broken. I have a spares bike and thought take that gear lever as a spare. No such luck, it won't come off. But if that happens up in the Alps your spare is no use.....
Fuel pump can be bought in UK for £50 and is correct fit.
Brake pads and tyres before you leave....
Alternator monkey nuts, brake fluid change, clutch rod boot.
One not mentioned, fuel hose. This perishes and hardens and cracks easily when disturbed. Replace them, cheap, use the BMW screw hose clips from the R series, they are neat and mean you can remove the gas tank if needed. Don't leave the old pipes, seen a lot of fuel leaks on Ks from old pipes. cheap. Then get 2 small off cuts about an inch long, seal one end with mastic. If you do have to take the tank off slip them over the spigots, keeps dirt out and no leaks.
Add some cable ties, electrical tape, some wire, Jubilee or worm hose clips, electrical connectors, spare bulbs. Spare brake pads, had friction material come off one of mine at a wheel change with only about 5k miles on the pads, seemingly not unheard of. Plus I have found my rear pads don't last as long as the rear tyre. Not caused by a bad disc, disc was new. On LT its easy to use a lot of rear braking especially touring and lots of weight on the rear. Lots of hills is harder on brakes.
Make a small list of contact numbers for people with access to workshop or K parts. Like some time back I got a panic call for a fuel pump. Had one on my shelf so the guy had one in a few hours. I let people take the parts and they order a replacement to be delivered to me but it means they don't have to await delivery. I send stuff to Europe and it generally gets there in 2/3 days on regular mail.
Get both wheels balanced too. In France you have a 130km speed limit as in 80mph and you will travel at that speed because that's what the traffic does. You will notice imbalance or low pressure. Important too is that one these roads it's a sustained high speed and its where the Ks really shine. Higher tyre pressures are normal for this, I use 38psi front 110/90/18 and 42-45psi rear 140/80/17 and it feels like on rails.
Some tyres while brilliant in dry conditions are less than perfect in wet conditions. Pilot Road 3 and BT 45 are 2 very common options here. I have tried most and now don't venture from the BT45 as I ride all year and would wear a set out over the winter. Excellent in the cold too. Lots of local K1100 recommendations though.
If you are going very soon don't go at anything major. Sounds like you have done most of the stuff anyway. The oil/water pump generally doesn't do a catastrophic fail but will start to leak giving you time to work out sorting it and to get parts if needed. I would not do it just a few days before going because it's one thing that can occasionally need a second visit. If working well leave alone for now. I went across Europe in a 20 year old car with a very minor coolant leak at the thermostat and was going to sort it and decided not to. I threw the parts in so I could sort it if needed but it was fine. Did it when I came back.
I have one of the tyre repair kits with the little gas cylinders. Never used it on the K but I have got others out of trouble with it so they do work and no slime. Essential travel kit in my book.
Sadly my tool roll weighs in at about 2.5 kilos or over 5 pounds weight. However I can do any task with it and it has been very useful.
Enjoy the trip and let us know if you will be making it to Ireland. I had a very pleasant evening two days ago with a K owner visiting from Surrey who wanted to sample some beer.
Because we live on an island ferry travel is our norm. So I bring my own tie downs for going on ferries. As in work out how the K will be tied down and have a cable tie to clamp the front brake to stop it rolling off the stand. Also have a tie from the stand to the front wheel. The second use is if you did need a recovery a lot of the recovery guys are clueless about bikes and especially about Ks. Lots of Mediterranean ferries from Italy across to Croatia and Greece etc etc.....Malta Corsica Sardinia and more.
A very useful thing is a bicycle type of lock, a long wire one with plastic coating. Run it through the carrier, tragkorb handles and across the pillion seat. When you go somewhere you can use it to lock helmet or bike gear through leg or sleeve or other stuff to the bike for a short time.
The advice about some small amount of oil is wise. On the motorway in Austria at a services I saw over €40 for a 1 litre oil. Lidl sell them for €5 and most places no more than €10. Depending on your packing a 500ml Coke bottle with oil in it is a very useful idea.
And don't use E85 gasoline....
If you get to Ireland be sure we get to see you. Very active K community here.....Safe travels too!