This is an implementation detail to be argued about to find a fair formula.

I thought your plan was simplifying things and getting lawyers out of it, guess not.

Again, this is a matter of determining a fair mathematical formula that rewards inventors appropriately depending on the amount of sales.

How is a fair mathematical formula determined?  Who decides what is appropiate?  Are sales the only metric for the formula?

Also, for comparison how does our current patent system ensure that inventors recoup costs on valuable patents?

The inventor licenses the patent for for an agreed upon value.  Value is determined by the market.

How does our current patent system reward downstream inventions and ideas?

See above.

You seem to have lofty goals for a new system that our current system doesn’t address.

How are those not addressed?

What patent fees? We’re talking about taxing products / services / corporate profits and then using that money to reward inventors.

Money that goes to patent holders is a patent fee no matter how the money is collected.  If a company uses a patented invention but doesn't list it how is that infringement enforced?  More lawyers and lawsuits?

Again, implementation detail, but if multiple ideas contribute to the same product then the inventors of both would get rewarded.

Details are the important part, how is the value of one patent determined over another, ie how do they split the revenue.