It seems that this is a typical problem, also discussed here.
12V AC after rectification should be plenty for the 7812 regulator. I think that using a 15V AC transformer is an overkill, considering the excess heat and the need for 25V rated capacitors which will probably not fit on the available PCBs.
Rectifying 12V AC should give almost 17V so that doesn’t sound right. I suspect that there must have been something wrong with the transformer, or you might have gotten one which had more loses than typical.
Of course, toroidal transformers are better/superior, but unless you are dealing with audiophile/high end audio, these features are not really needed in a modular synth. Many (most?) modular synths even use switching PSUs and they perform fine, so I regard using a toroidal transformer in a synth PSU an overkill.
I mean, I am not to tell people how to spend their money, but just saying for the sake of the discussion since other people are probably reading this 
Personally, I use a regular 12V AC (rated 30VA) transformer (made locally by Amarad and sold with the intended use of… heating beehives) and the 7812/7912 regulators PCB by Arthur Saunier. I built two of those without any startup or noise problems.
I recently got a high end toroidal transformer by Giatras, but will likely not use that on a synth PSU. I am thinking it could be more useful in a (tube) amplifier project.