You're underestimating the sheer size of the RN though Blondie. Even without Dreadnoughts the sheer number of ships the RN can send to fight america without weakening the fleet against the small forces of the German fleet are staggering.
Lets take this dust up as happening at the same time period as the 1905 Russo/Japanese War in Battleships alone you've got this going from oldest to newest.
6 Admiral Class Battleships in Reserve
2 Nile Class Battleships in reserve
1 Victoria Class Battleship In reserve
8 Royal Soverign Class Battleships
2 Centurion Class 2nd Class Battleships
1 Renown Class 2nd Class Battleship
9 Majestic Class Battleships
6 Canopus Class Battleships
8 Formidable Class battleships (basically the same ship as the Misaka, flagship of the Japanese Fleet at Tishuma)
6 Duncan Class Battleships
2 Swiftsure Class Battleships
5 King Edward Class Battleships with 3 more under construction.
A grand total of 56 Battleships. And the reserve ships were in perfect condition only needing coal, ammo and crew. All the rest were in service, fully manned, fully deployed.
Then you're talking hundreds of Cruisers, armoured, protected and light, then hundreds of Destroyers and Torpedo Boats.
The RN could contain the HSF with the Channel fleet, re-deploy the Med fleet, pull together the Afraica, India, Far Eastern, South American, North American (west coast and East coast) squadrons together and go against the USN.
Lets compair to the German fleet
4 Brandenburg Class Battleships
5 Kaiser Fredrich Class Battleships
5 Wittelsbach Class Battleships
2 maybe 4 Braunshwig class Battleships with 1 more under construction.
The USN
1 Texas Class Battleship
3 Indiana Class Battleships
1 Iowa Class Battleship
2 Kearsage Class Battleships
3 Illinois Class Battleships
3 Maine Class Battleships
5 Virginia Class Battleships fitting out, launched in 1904.
For a combined total of 34 Battleships, although you might as well discount the Brandenburd Class and the Texas as both were basically coast defence ships, poor range, poor sea keeping, next to no secondary armament to keep them safe from Destroyers, Cruisers and torpedo boats.
Please do not be under any illusion that the Germans could tie down the RN or that the RN would be overwhelmed by the two fleets.
It is interesting you pick 1905, which is really the peak year for RN relative power. This shows how the dreadnought class, while a great idea, actually made more British ships obsolete than UK ships. I am not double checking your numbers.
You show sixteen German ships, and with the UK idea of keeping 2-1 odds, it keeps AT LEAST 32 ships at home. Now the remaining 22 UK ships to 18 ships is close enough the battle will be close call, but likely the USA dominates near its ports and the UK near its ports. Now remember, you picked the peak year of UK relative strength, so you have to have the political situation. France's traditional enemy is still the UK. If the UK ever loses control of the seas for a few weeks, the Sealion can happen, and the British empire will end. So the UK likely keeps well over 32 ships in its home port. Also, the UK ally helped maimed France's critical ally, so you probably picked the worst diplomatic year to start a war for the UK.
The hundreds of cruisers will be chasing AMC's all over the world. They also will be handling the surge in submarine construction. Look at what one ship the SMS Edmen did. The USA/Germany combo will be able to put out hundreds of AMC, and they will have to ports to resupply them.
You comment of pulling ships is double counting. You can't start a list of the entire British Navy, and then also talk about pulling out ships from other seas. You should either start the analysis with the Ships in home waters combined with an analysis of the ships that can be pulled from other fleets. Or you can just assume they pull them all, and start with a total list.
And also, Canada falls. The only question is does it take one or two years for the USA. And I never said the USA sweeps the seas of the UK, but that the UK can't win the war at sea, only lose. Even if the UK sinks the entire USA and German capital ships at 2-1 loss ratio in favor of the UK, the UK still lose Canada, and the USA keeps building ships, so does Germany. So after the initial surge of fighting, even in a UK wank, it is either a negotiated peace or a long war that as likely break the British Empire as result in a British win that increase the power of the UK.
And it is nice to say the UK has "better sailors, better admirals", but WW1 and WW2 show the UK both wins and loses, even when it has noticeable advantages in ship numbers. It is a nice story the RN never loses a sea battle, but it lost a lot of them, but normally it had both a bigger Navy, a better port system, and a bigger ability to replace ships. In this war, it starts with a slightly larger navy, but the other side will build ships faster, and the USA/Germany have a better terrain for the war. Unless you think a Philippine /Hawaii for Canada is a good strategic trade, the the UK comes out badly in this war.
Now as in most major wars, who are the real winners? The great powers who did not fight. France will likely negotiate favorable treaties for its favors as quite possibly would the Ottomans, Italy, Spain, etc.