@NorCalGal 

"How are monthly payments to the credit card recorded to pay as the Fixed Asset is paid down? Do you split the payment somehow, just record it as a general expense, record it some other way?"

From an accounting perspective, there's no connection between monthly cc payments and the fixed asset that was charged to the cc.  Monthly payments just reduce the cc balance.  You already recorded the fixed asset at the time it was charged to the cc.