I think the Solera system of aging and maturation is a little ambitious when using such small barrels and I'm not sure this system will work with high strength alcohol.
There is a reason that Bourbon distilleries are only allowed to use barrels once. When a high ABV spirit is aged in an American White Oak barrel there's not much of anything left in the wood when the spirit is removed.
The Solera system is used in the aging of fortified wines and sherries rather than high ABV spirits because they don't strip the wood of everything and leave certain substances behind which help mature and even out the younger wine or sherry to maintain consistency.
If you have three barrels fill them all at the same time and follow the aging/dilution regimen I described and you'll end up with a reasonably good Bourbon
type whisky.
To make proper Bourbon Whisky (there are no no
e's in Bourbon

) you have to make the spirit from grain, mainly Corn (Maize) Malted Barley and even a little Rye. There are different recipes depending on which distillery you follow.
I considered using this type of barrel myself in the past but my research found that they have a limited life. After aging one batch for 9-12 months you can add another batch but it will take substantially longer to achieve anything like the result from the first batch. Wiser heads than mine suggested it could take more than 2 years for a second batch to achieve anything like the quality of the first batch in the same small barrel and even then there would be no guarantee.

Rather than putting my spirit
IN American White Oak I put the American White Oak
IN my spirit, in small pieces, and store my spirit in 2 & 3lt glass jars like this...

I'm currently sourcing Stainless Steel Cornie Kegs like this...

...these have a capacity of 19lt and I can put whatever amount of Oak I need in the spirit and when it's done I can bottle it and reuse the kegs over and over. Cool or what?

Anyway, good luck with the barrels whatever way you decide to use them.
AM
