My forestay tension is far too slack, tightening the backstay doesn't help. Shrouds checked by rigger. Not sure where to start. Inner forestay too tight?
Strongly suggest reading the Selden bible (every sailor should, it's really helped my understanding of standing rigging):
HINTS AND ADVICE on rigging and tuning of your Seldén mast.
To give you advice, we need to know more about your rig - from your website, it looks like the standard Bavaria 7/8 fractional rig. You say you have an inner forestay, which is not standard although a removable was available as option. That can always be safely slackened and then you can play with cap shroud and backstay tension and see if it gets your forestay less floppy. There is an optional integral turnbuckle available for the 300S, which is hidden inside the drum if installed. This is rarely adjusted though and only used to tweak mast rake.
On your photo I only see a babystay, which would not cause this, unless it was seriously shortened and then it would give the mast top an extreme aft bend that you'd surely have noticed.
Did the rigger know that these rigs are high tension rigs and the cap shrouds (on the fractional with swept spreaders configuration) must be tensioned to 20% of their breaking load (25% with the backstay slackened off). In my experience several riggers were not aware of this and simply "tightened it up a bit" like a traditional rig... to be tensioned appropriately later, under sail. If you find one with a tension gauge, write down the numbers and compare them to the recommended tension in the Selden bible. Most likely there'll be not nearly enough tension on it - winding it up to the recommended 20% (with backstay tensioned and thus relieving the cap shrouds) on my 10mm wires took serious grunt and well oiled turnbuckles.
If you want to do it all properly, read the manual, then loosen the entire rig (equal number of turns both sides to keep mast centered) and then do it all up to recommended values using the wire stretch method. If your rig has ever been replaced or fiddled with, it is most likely set up wrong. Keep in mind there is no such thing as a certified yacht rigger