After war with Japan broke out only 3 British battleships were sent to the US for refit (I'll exclude Warspite which was already at Mare Island from Aug 1941 until Jan 1942).
Queen Elizabeth (already modernised) from Sept 1942 to June 1943, following the extensive damage she suffered at Alexandria in Dec 1941.
Royal Sovereign from Oct 1942 to Nov 1943. Following that she returned to the UK where it was found she still had defects in her main armament ammo supply system, which it was felt were not worth repairing. So she was laid up under Care and Maintenance at Rosyth before being transferred to the Soviet Union in May 1944 in lieu of one of the Italian battleships.
Nelson from July 1944 to Jan 1945. Friedman however, on my reading, notes that the completion date kept moving to the right but does not explicitly state it was because the ship was in worse condition than indicated. That may or may not be true but there was clearly more to it.
As early as July 1943 the Admiralty were noting that the USN was reluctant to undertake long term repairs on what they considered to be "old ships", very probably as a result of the experience with Royal Sov. The Admiralty put the case that the Nelson was younger and that it was a case of "outfitting a powerful and relatively modern battleship" that still had its original armament. Rodney was to be refitted at Devonport. A plan was then agreed to refit Nelson in the USA with 5"/38 guns and Mark 37 directors amongst other improvements. In July 1944 completion was estimated to be Dec 1945 which slipped to mid 1946 by the end of that month which Admiral King then stated as end of 1946 and offered a compromise of Sept 1946! King effectively killed the project in Oct 1944, by the use of a little considered provision in the Lend-Lease Act that required US approval for all finished equipment and materials for the refit. Britain lacked the resources to provide all the necessary paperwork which was normally the function of the Planning Dept of the Navy Yard (see note 60 on page 402 Friedman British Battleships quoting documents in Nelson's Ship's Cover). The cost was to be capped at $3m. As this was unacceptable to the Admiralty a new minimal scheme had to be worked out to get the ship back to sea around the end of 1944 (it slipped to Jan 1945) when she returned to Britain for further work before heading to the East Indies Fleet to replace Queen Elizabeth as flagship.
So regardless of the condition of Nelson in July 1944 there was a definite USN (or at least Admiral King) bias against refitting the ship in the first place. This was then compounded by events in the Pacific in Oct 1944 that saw the cruisers Canberra, Houstoun and Reno all torpedoed and sent to East Coast yards for repair, albeit that none arrived for several months and none ended up at Philadelphia NY where Nelson was refitting.
It should also be noted that the French tried to get Jean Bart refitted in the USA in 1943/44. In May 1943 the USN agreed to repir her sufficiently to allow her to travel to the US probably around Sept 1943. Plans were worked out for a one turret ship with 340mm guns from the Lorraine and a massive AA armament of US weapons. The French request was turned down in Aug and they made a direct approach to King in Dec. He took until March 1944 to inform them that the USN was unwilling to divert resources to the ship. Again given the extent of the work it would have had to go on until late 1945 or into 1946.
Rodney was in a far worse state than Nelson having missed out on a refit immediately prior to the war. When finally laid up in Nov 1945, the story goes that her pumps had to be kept running continuously to stop her filling with water such was the state of her hull!
It is also interesting to note that the USN continued to refit its old battleships in this period. West Virginia didn't complete her rebuild until July 1944. And Arkansas, New York and Texas were all sent to the Pacific in late 1944/early 1945 being given such repairs as necessary.
Edit - re the laying up of Royal Sov, it did occur when the RN was feeling a real manpower shortage which resulted in many older ships being laid up. That probably influenced things. Pity the US effort on the year long refit was wasted.
