Rather than get into a debate over the risks of aggressive capitulation I'd rather just ask how you would go about handling the stick portion of the donkey motivation metaphor. So far as I am aware Amtrak already has the carrot covered.
The REAL problem is the "carrot."
Here's the thing about attempting to muscle and/or bribe a company that has money: they don't care. CSX would rather spend their own money and be free of passenger service than take the carrot and be stuck with passenger service. The "threat" of fining them means nothing if they can make more running their own trains. During the 1990's, an officer in CSX once famously declared how much he disliked Amtrak and would rather pay the fines.
One of the things Amtrak can do is be consistent with the help and be prepared to heavily invest in your partner's infrastructure.
Along with that, when hosts are threatening to reduce capacity, the states and Amtrak should step up and assist with the improvements, and demand strict accountability for their efforts. A perfect example is when BNSF wanted to get rid of the Devil's Lake Sub, the FRA, Amtrak and BNSF split the cost of improving the line. If I'm not mistaken, Maryland contributes to CSX's Old Main Sub to alleviate pressure on the Metropolitan Sub, which allows MARC trains to run with less interference.
However, that only works if there is an actual interest in a mutually beneficial relationship.
BNSF is extremely helpful because they look at the performances incentives as income. It is free(?) money to them. As previously mentioned, what good is money, incentives etc to someone that is indifferent (at best) or downright hostile (at worst) to your presence? All the money VA put into the former RF&P sub to expedite the movement of passenger trains means nothing if CSX refuses to cooperate.You can fund improvements, build bypasses, put in switch heaters, or even give them your interpretation of fair market rate. If they aren't interested in the carrot, it remains just another excuse.
Call it what it is. Some people aren't interested in the carrot. Knowing that, you have two real choices. Hope someone with deep pockets will assist you with establishing an incentive program that will improve capacity and make the hosts feel as though you're a partner and not a squatter. The other choice is to hope someone with legislative chops can terrorize the hosts into cooperation. However, the barn door to that was partially closed when the railroads were allowed to reduce capacity.
I'm afraid the only stick we can find is too small to motivate the donkey. So, now we must find a big enough carrot to feed it...because in the spirit of honesty, if I operated a freight line, I would appreciate the extra money Amtrak paid for the maintenance/inspections that allowed me to operate at a higher speed. However, before I decided if the Amtrak or my freight would take the siding, I'd definitely look at the balance sheet.