Except for Brightline wanting to use CFX's right-of-way and so having to reach a financial arrangement with CFX, what is the basis for Brightline having to "compensate" Florida DOT for "lost" tolls?!*
None. It has to do with Brightline getting permission to lay their tracks on CFX governed FDOT land. It has to pay a fee to CFX and CFX and Brightline jointly deciding what it should be per passenger carried along the CFX segment. Brightline has to work with CFX when it wants to add additional origins and destinations to determine what the passenger fee should be.
Presumably the same principle will apply for trackage along SR417 Tollway.
As for what financial arrangements will be used for leasing space on I-4 median, it will probably follow the same principles used for leasing space on the portion of SR528 that is not under CFX but under FDOT (i.e. roughly east of the SR520 interchange). I am not sure what the details of that arrangement are, but AFAIK (unless it is covered by the CFX toll compensation) it is not a passenger volume based fee, but is probably some flat annual fee.
The reasoning behind all this goes as follows: SR528 and associated ROW development including stabilization of it across marshland, was funded using bonds that were collateralized by tolls. Now what amounts to additional "lanes" are being added to it in the form of a rail tracks, which will eat into the original tolls that were presumed to pay off the bonds. If these new non-toll paying lanes diverting toll paying traffic were to cause shortfall in bond payments the state would be obligated to pay such through general funds, while the financial advantage ensuing goes to a private company. This was not a condition that the taxpayers were presumed to agree to. Hence the toll compensation for use of land that was originally developed using bonds that were collateralized by income from said land improvement. It is as simple as that.
None of the other examples quoted above come even close to being similar to this situation.
What if Amtrak began running more than one round-trip daily between Tampa and Orlando, would it have to "compensate" CFX or FDOT for "lost" tolls? And what is a "lost" toll? Is it presumed that every Brightline passenger between Tampa and Orlando is a lost toll? Every family or traveling party?
That question is almost moot since (a) there is very little toll (short segment of SR417 between CFRC and I-4) between Tampa and Orlando. (b) I am sure Amtrak will get to pay their salutations to the ROW owner CSX and CFRC (indirectly FDOT). CFX has nothing to do with the facilities used by Amtrak to run its trains between Tampa and Orlando.
But Brightline I am sure will have to make some land use lease payment for putting its tracks on FDOT land in the I-4 median. The state could choose to make it something small, but it is a lease of land.