Welcome aboard!
First the test depth of the Salmon was about 250 feet, probably deeper than the harbour.
Second what was your approach path? Were you taking advantage of the terrain? Trying to sneak down the center of a channel is not always the best. In some cases it may be better to sacrifice depth for getting a little closer to the shore.
Third, always try to keep either your bow or stern pointed at the destroyers. The "thinner" your aspect to them the harder it is for them to detect you.
Fourth, 4 knots is a bit fast. At 1/3 speed you may have popped out of silent running. Try getting down to 1 knot.
Fifth, when sneaking past DDs, try to figure out that pattern of their patrol and identify a time when both are looking the other way. Subsims are a stealth game. You are going to spend most of your time waiting and watching.
Is there anything in your orders that say you can't sink the destroyers? I am being serious. At periscope depth you are actually harder to detect on active sonar. Maybe consider a night approach and create a "distraction"?
If the DDs are picking you up at 8,000 yards, you are broadcasting something.
Good luck with it and welcome aboard
