I'm not well versed in this topic, just speaking out load to try and gauge some further interest...
If you did it through the company, you would get the 4K deduction on your flow through personal income tax which would be similar as just paying it with the HSA which already saw the income tax break. Paying with the company could maybe help you stay in a lower bracket if that's a need. However, what's your goal of your HSA? To help fund retirement or pay for medical expenses?
If the medical expenses are 100% deductible through company, I'm leaning that route to reduce taxable profits... and either investing the HSA or holding onto it when you may need it later.