What did the Baltic Fleet do in Reval in 1904 and when was it there?

I think I've been able to piece together an answer, mostly thanks to @MoisheKohan whose comment on my post above led me to some wonderful sources. This answer is based on Худяков's [Hudjakov] «Путь к Цусиме», Саркисова's [Sarkisova] «Путь к Цусиме. По неопубликованным письмам вице-адмирала З.П. Рождественского», and personal comms with historian David Vseviov. Sarkisova draws on previously unpublished Admiral Rozhestvensky's personal letters to his family.

Russian translations are via Google but with modifications; input is welcome as I suspect there are numerous corrections that could be made.

Summary

Overall, it looks as if most of the delay was unintentional and caused by failing machinery and poor seamanship. Given there was a ceremonial send-off in the beginning of September, the Imperial Review in the end of the month—immediately after which the fleet sailed—sounds like an add-on to the original plans which were likely amended due to some ships not departing Kronstadt with the others.

Timeline

Note these are in the Old Style; New Style is +13 (conversion by myself). Mostly as my sources are Russian here so their dates are OS while the question used Western/Japanese sources that would have been using NS.

Specific events that are mentioned:

• The Baltic Fleet left Kronstadt for Reval on 12th August 1904 [NS: 25th Aug];
• A ceremonial sending off by the Emperor is mentioned on 30th August 1904 [NS: 11th Sep]
• The first letter by Rozhestvensky from Reval is dated 4th September 1904 [NS: 17th Sep];
• The Dowager Empress visited the fleet sometime between 5th and 20th September 1904 [NS: 18th Sep and 3rd Oct];
• The second letter by Rozhestvensky from Reval is dated 20th September 1904 [NS: 3rd Oct];
• The third letter by Rozhestvensky from Reval is dated 25th September 1904 [NS: 8th Oct];
• The Imperial Review took place on 26th September 1904 [NS: 9th Oct];
• The Baltic Fleet left Reval for Libau on 27th September 1904 [NS: 10th Oct];
• A letter by Rozhestvensky from Libau is dated 1st October 1904 [NS: 14th Oct].

Activities at Reval

Ceremonial Send-Off

_{В нем описание церемонии проводов эскадры. Ее выход в плавание к японским берегам был обставлен торжественно. ... Кроме того, уже в Ревеле стали появляться проблемы, которые становятся темой практически всех остальных писем, – постоянные поломки, выход из строя машин, слабая дисциплина на кораблях.}

_{«Я был очень рад видеть всех Вас … в прошлое воскресенье, и очень жалел, что Вы повернули так рано, не видели, как собрались разбросанные отряды, как вошла в ряд Царская яхта, как красиво вышло прощанье.}

_{В Ревеле неделя прошла незаметно, но нельзя сказать, чтоб очень удачно: постоянные поломки машин, электромоторов, непорядок на судах… и часто непокойное море мешают учиться многому, что было намечено.» [Sarkisova]}

It [the letter] describes the ceremony of seeing off the squadron. Her sailing trip to the Japanese shores was arranged solemnly. ... In addition, problems began to appear in Revel, which became the topic of almost all other letters - constant breakdowns, failure of vehicles, poor discipline on ships.

“I was very glad to see all of you ... last Sunday, and really regretted that you left so early, did not see how the scattered troops gathered, how the Tsar’s yacht entered the roads, how beautiful a good-bye it was.

“In Reval, the week passed unnoticed, but it cannot be said that it was very successful: constant breakdowns of machines, electric motors, disorder on ships ... and often the turbulent sea interferes with learning much, as was planned.”

Waiting for Late Ships

_{Въ немъ все еще недоставало транспорта "Камчатки" и броненосца "Орель": у 1-й передъ самымъ уходомъ были испорчены машины, а 2-й все еще был не готов. Броненосець "Орел" быль сначала умышленно затопленъ въ кронштадтской военной гавани; а затьмъ за нъсколько минутъ до пробы машинъ было открыто, что въ подшипники наждачный порошокъ, чтобы испортить машину при же пусканіи ея въ ходъ ("Море", 1906 г., № 5, стран. 178). [Hudjakov]}

They still lacked the transport "Kamchatka" and the battleship "Oryol": the machinery of the first was damaged before leaving and the second was still not ready. The battleship "Oryol" was first deliberately flooded in the Kronstadt military harbor; and then, just a few minutes before the test, it was discovered that there were [?] powder bearings in order to spoil the machine when it was started ("Море", 1906, No. 5, стран. 178).

Repairing Ships

Some of these were partially due to Reval being a very shallow harbour.

_{Наконецъ пришли "Камчатка" и "Орель"; адм. Бирилевъ пріъзжаль въ Кронштадть самы, когда броненосець, утопавшій и оправившійся, опять вдругъ сълъ на мель за две недели до похода… [Hudjakov]}

Finally came "Kamchatka" and "Oryol"; Adm. Birilev himself led from Kronstadt, when the battleship, wallowing and recovering, again suddenly went aground two weeks before the campaign...

_{«...Теперь пока учимся, да поправляем несчастие с транспортом Иртыш, который умудрился в штиль в полдень на Ревельском рейде пробить себе дно на камнях зашедши туда где ходить ему отнюдь не следовало.» [Sarkisova]}

“...Now while we are learning, let’s correct the misfortune with the transport ship "Irtysh" which managed to break its bottom on the rocks of the roads of Reval when they went where they should not have gone.”

Visit by the Dowager Empress

_{В нем − описание посещения эскадры матерью Николая Второго вдовствующей императрицей Марией Федоровной и королевой Греции. Высокие особы очень торопились, и по-настоящему сердечной встречи не получилось. [Sarkisova]}

It [the letter] describes the visit of the squadron by Maria Fedorovna, the mother of Nicholas II, the Dowager Empress, and the Queen of Greece. High leadership was in a hurry, and a truly cordial meeting did not take place.

Waiting for Final Orders

_{Здесь эскадра собиралась «в кучу» и ждала решения о выходе в плавание. [Sarkisova]}

Here [in Reval] the squadron gathered "in a heap" and waited for the decision to sail.

And as written by Rozhestvensky on 25th September, one day before the Imperial Review. In the letters, the Admiral also decries in the strongest terms that they had been waiting for so long, allowing autumn weather to set in.

_{«... Завтра здесь должен решиться вопрос о том, когда нас отправляют.» [Sarkisova]}

“... Tomorrow the question of when they send us from here should be decided.”

Imperial Review

_{...эскадра въ Ревель ждала Высочайшего смотра. [Hudjakov]}

...the Reval fleet was waiting for the Highest Review.

_{В письме рассказ о посещении эскадры 26 сентября в Ревеле императорской четой. Рожественский, естественно, сопровождал царствующих особ и давал объяснения по ходу бесед с командой своего флагманского корабля − только введенного в строй эскадренного броненосца «Князь Суворов». Однако о Николаем II он не упоминает ни словом. [Sarkisova]}

In the letter, there is a story about a visit to the squadron on September 26 in Reval by the imperial couple. Rozhestvensky, naturally, accompanied the reigning persons and gave explanations in the course of conversations with the crew of his flagship—the newly commissioned squadron battleship “Prince Suvorov”. However, he does not mention a word about Nicholas II.

Once in Libau, the squadron refuelled before steaming off a few days later.