Everyone hating him is really a lot due to the extreme propaganda against him from the plotters after the coup - while a bit out of sync with his times, being very religious and believing the "King by God's mandate" absolutist stuff, he was not really that bad nor hated.
The Russians were in a dire situation several times during their Finnish campaign. if the threat from the south melts away faster (which I think it would, commanding Danish and Spanish troops was not a high-priority position, it would nopt be given to any of the more superb French generals or marshals), Sveaborg could perhaps be reinforced, or at least the Army in Finland responsible for delaying the Russians until reinforcements could be sent.
I have read that part of the reason Cronstedt decided to durrender was that he was sent to Sveaborg as a punishment as he was out of favour - it was seen at the time as a position away from the real decisive battles - the King valued the Swedish-speaking parts of Sweden much higher and saw the threat from Denmark and Norway as more of an emergency - which is logical, as the Russians were expected to be unable to get past Sveaborg, and in spring the archipelago fleet would wreac havoc upon the Russian coastal shipping, instead of being captured and used the other way around. If focus was more on the east due to the Spanish force melting away, Cronstedt would probably be replaced and put in a position where he could do less harm.
If Sveaborg does not surrender, the British will probably deliver 10 000 men as promised, and big naval support. The Russian navy was about at parity with the Swedish, and the Danish one Nelson dealt with earlier so with British support, the Russians will stand little chance at sea.
on the alnd front, the Russians had serious problems supplying their troops, and part of them melted away, the spring was very harsh 1808 (the ice did not melt outside Sveaborg until mid-May).
Perhaps you are right that Viborg is out of the question, even if Sveaborg is held, but the 1721 border should be possible, methinks. This would make Gustav IV Adolf victorious and silence the nobility that did not like him and the defeatist noble officers' corps. Being on the victorious side in the Napoleonic wars from the beginning could probably net Sweden some land somewhere - perhaps all of Norway, as historical, while keeping Finland, and some prestige for the King.
The crown prince would live to become an Austrian general of some importance, it would be interesting to see if he had urged a Swedish entrance (from a more powerful position) into the Crimean war.