If you switch branches with no break in service (ETS-my branch won't release me), do you get to keep the pension system (compared to BRS)?

The system is based upon DIEMS (Date of initial entry into military service); if you didn't elect BRS in January of 2018, you won't get enrolled into BRS when you change over to the Air Guard. The automatic enrollment into BRS is for first term, initial entry ascensions (those whom never served and are serving for the first time in the Armed Forces).

That probably won't work out as you are planning. There is preparation that is required for processing enlistments and reenlistments and the ANG will need your NGB22 at the minimum. Knowing the Guard, you probably won't ETS with it in your hand.
As for your original question, you get to keep the legacy retirement. You will have one year after you join a new component to switch into the BRS if you chose.

If you have IRR on your contract, i.e. 6 and 2 or or 4 and 2, then you can talk with your IRR counselor to help you with the process of transferring into the Air National Guard. As for the state to state transfer that will be something that you will have to contact the state command to gain more information. However, keep in mind that you can also consider getting an aviation job in the Army National Guard if your state has the MOS available.

Also, it maybe easier to talk with your current state's Air National Guard to gain the transfer from Army National Guard to Air National Guard, then take the state to state transfer option. To be honest this is really a state command issue and I would run the rabbit that direction if the options I stated are not available.