On and after December 26, 2007, funds available to conduct appeals under section 1205(c) of the 1968 Act [34 U.S.C. 10285(c)], which includes all claims processing, shall be available also for the same under subpart 2 of such part L [34 U.S.C. 10301 et seq.] and under any statute authorizing payment of benefits described under subpart 1 [34 U.S.C. 10281 et seq.] thereof, and for appeals from final determinations of the Bureau (under such part or any such statute) to the Court of Appeals for the Federal Circuit, which shall have exclusive jurisdiction thereof, and for expenses of representation of hearing examiners (who shall be presumed irrebuttably to enjoy quasi-judicial immunity in the discharge of their duties under such part or any such statute) in connection with litigation against them arising from such discharge: Provided further, That, on and after January 2, 2013, as to each such statute—