I think it would be best to get a fixed set of teams, rather than go for promotion and relegation. The NFL is one of the best examples of a stable sports league.
If FOTA were to buy FOM in a formation of the Premier League style coup, with fifteen F1 teams getting equal shares of all the TV revenues, collectively done sponsorship (which needs to be exploited more) and other things.
However, the F1 derived F2 idea you propose could work IMO. The key parts of what I propose for F1 can be summarized as follows (I'm not going to post my full "manifesto", that can go elsewhere).
- Bodywork extremities made of GRP aside from crash structures, reinforcement of the spirit of the new aero rules by specifically banning use of things like mirrors and crash structures as aerodynamic devices, metal suspension like F3. Road relevancy and cost control.
- 640kg, minimum weight for driver+seat, no more than 5kg of movable ballast. We don't want the drivers like jockeys.
- Six race engines, 800hp power limit and restrictions on gimmick technologies not found on that manufacturer's road cars, otherwise free with fuel economy incentives for manufacturers. Must supply price for engines of around £75,000. KERS to be included in the engine for this purpose. No part of the powertrain may be made of composites.
- Spec telemetry and data logger, with all data made available to everyone (including press and other teams). This includes a heart rate monitor on the driver - yes, a bit like The Chair. No adjustable power control type systems (fuel mixture, launch maps, adjustable turbos and similar cowpoo) aside from pit limiters and a fuel save mode that is restricted to SC periods only.
- Single fuel supplier, providing any non-diesel like fuel requested by manufacturers. LPG, E85, straight out petrol, hydrogen, whatever.
- Larger cockpit openings, fitting a larger than average dummy like Formula SAE and must be adjustable so that a smaller than average dummy is able to reach the pedals.
These would largely cut costs in areas like engines (where manufacturers would be able to spend as much as they like and get no advantage, and privateers buy them cheaply) and a reduction in chassis costs. If need be, a budget cap could be done on the things that affect performance - but not engines, as they are the most realistic thing for road relevant technology development; and my plan would make then equal in performance but still produce technological warfare.
Then, you could detune the engines to ~600hp, replace the KERS (possibly with an "overboost" button to simulate it) get rid of some of the CF and replace it with GRP, stick harder tyres on - hey presto, F2.
You would have two lots of development for the price of one, as new cars from the ground up would not be needed - like Dallara's Formulino thing that goes from something like an FFord to something just below F3. As the series should be about the drivers, maybe do a (and I appreciate that some of the purists will want to make me drink my own genitalia for suggesting this

) GT3 style equalisation test for F2, but not F1 of course. That would make a great breeding ground for F1 drivers. F1 indies would be required to sell F2 cars to teams, with the mountings ready for two different engines - these being subsidised by F1's and F2's income.
If the second tier of football in many countries has a following, the world's second tier of motorsport should be able to get one.
Perhaps I need to lay off the strong cheese at night,
Dukeage.