I think your logic is sound but perhaps your syntax is off. So my two tips below:
1) Try to start simpler before adding more punctuation?
2) Also, sometimes I like to take my calculation out completely, save the blank field, and add the calculation back in. :)
Ideal calcs of this nature would start off like this:
SUM(IF(Field1=True,FieldAmt1,0),IF(Field2=True,FieldAmt2,0),IF(Field3=True,FieldAmt3,0))
i.e. in the simplest case where field names are one-word (super short and simple), you wouldn't have needed any additional fluff.
Even in this particular case, I haven't found that there's a problem between doing the above calc, and doing the same calc as a multi-word fieldname. But if I did have a problem, I would have definitely tackled it the way you did (curly brackets). However, I don't see a need for the additional parens at all--so those and the equals sign at the beginning might be messing you up. Your end result would look like this:
SUM(IF(Field 1=True,Field Amt1,0),IF(Field 2=True,Field Amt2,0),IF(Field 3=True,Field Amt3,0))
PS: usually I save the curly brackets for if I have punctuation inside my fieldname.