Correct call?

[Andy]

If I am reading this correctly....

I've got a dead ball, two base award.
Prior to the appeals, two runs score, R3 now on third, R4 now on second

After the appeals and if the appeals were upheld,

R2 declared out for missing 3rd, that run is removed.
R4 declared out for missing first, removed from second base.
Appeal on R3 missing home is moot, as stated in the OP.

End result:

One run scores, runner on third base, two outs, B5 at bat.