Not the supply services per se, rather shipping and deploying in country with a bigger army.
Your going to have to do better than this. The British managed to move and deploy six divisions OTL. The added 14 are not going to be difficult
1. Shipping? Really? The largest merchant marine in the world and the British are going to have trouble finding shipping for an extra 14 divisions to go across the channel?
2. Deploying in country? Really, the British are going to be in a friendly country where the civilian authorities are helping in every possible way. The Germans managed to deploy six times as many in hostile territory.
Don't forget that the threads assumption is that the British have years to solve these problems. Not every change is going to help the Kaiserreich
It is not so much a question of size as intent. If the British beef up their Army in any way that signals an intent to intervene on the Continent that will be significant. The Germans were painfully aware that by their own formula they were short 8 corps (or 16 infantry divisions plus supports) of the margin that they felt was required to ensure the defeat of the French. If the German decision makers had not convinced themselves Britain would stand aside it unlikely they would have been so enamoured of sticking their fist into the tar baby that a France supported by the fiscal and naval might of the British Empire would become when they had a reckoning with Russia to attend to.
Under German assumptions of the time France has to be beaten in 40 odd days if the troops are to become available to fight the Russian steamroller. Now we know that the Russians were not as fearsome as imagined but they were the driving factor in German calculations. The British can have all the numbers in the world but if the Germans still expect them to dither and do nothing they will likely roll the dice in order to beat the chimera of Russian rearmament . If the British do look like they mean to jump in from the start then the Germans may well blink before they commit themselves to war rather than waiting till the Marne battles as per OTL.
The Kaiser never doubted for a second that the British intended to intervene. On July 29 , he wrote "this means they intend to attack us." The British problem wasn't that the Germans doubted the British would intervene, and they really expected to fight through Belgium as well, they didn't care. The British Army was small enough that the Germans hoped that they could still beat France. It was as much hope as reason. The had, correctly, realized that beating France was their only hope as all east first scenarios would mean certain defeat
To prevent the war though, the British are going to have to
convince the Austrians that:
1) Britain will intervene and
2) that intervention will be decisive.
that the Austrians wouldn't have to fight the British makes these very hard
Probably coastal defences. Bulk up the battery in Dover. Early ww1 before the Dover Barrage was laid (minefield) the predreads were used to escort troop convoys in the channel. Bulking up the shore batteries may be the cost of getting rid of the Predreads.
I like your idea of getting the money from scrapping some of the older ships. They had limited use and would be of no use in a short war. Scrapping one old predreadnought and older armored cruiser for each division would provide more than enough artillery to transform them into a powerful force. That would mean 24 6inch guns and 96 smaller ones. That's far more firepower than a German division