Yes one thing you did wrong is watering the tree in Virginia,and if you fertilized it that is another cause why they have no flavor.
Apply minerals,like Dolomitic limestone,that is what it needs not water in Virginia.
Conadria is a relatively low flavor hybrid made by Ira Condit.
He used a very flavorful cultivar called Adriatic and a male caprifig and the result was Conadria ,a hybrid with less flavor and taste compared to the Mother tree,Adriatic.
We can't ask him what was in his head when doing so,because he is dead,but it doesn't make sense to me to do selection work and select an inferior specimen than what he started with,and then consider it an accomplishment,and slap his name on the new hybrid too.
If you like a white fig,get yourself an Adriatic,especially (JH Strain),and then you will experience Flavor taste and sugar,of the highest quality.
You will dig out your Conadria the first time you taste Adriatic(JH),and trow it in the dumpster like I did.

Thank you, Herman. I'm going to take it off the watering system, and consider digging it up for compost.

What I really want is a very sweet fig for eating dried. Reading here it seems like I want one of these: Celeste, Adriatic, kafirs, Sierra

It's probably not too late to get something in the ground, right?

Adriatic is the best,but Adriatic from UCDAVIS collection is too sick with fig mosaic virus and will not produce a good harvest.
Read my leaps:Plant JH Adriatic,in your climate and you are going to thanks me forever.

I too am looking for a sweet fig to dehydrate so where can one find an JH Adriatic tree?

Trees of antiquity dot com has a fig they're call Adriatic but it looks exactly like the fig that Groworganic dot com is calling Desert King? Is this an Andratic fig or Desert King fig? And would it be a good fig for drying?

http://www.groworganic.com/fig-desert-king-standard-potted.html

Here is a link that might be useful: Trees of Antiquity

Only People on this Forum have it.
You will not find it in any large retail nursery.
If you find one at nursery,ask if it is from John Hood origine,and hopefully they will tell you honestly ,yes or not.

Here it is,and how it must look.
Of course pix is bad,taken now in the dark,but you can see some leaf details.
I mhave four young one and keep them all.

JH Adriatic is a Forever Fig because it will probably stay in my collection. Excellent even young.

My Conadria fig is one of my many 'keepers'.