Difficulty to find any preimages $a$ and $b$ for given $V$ so that $H(a) \oplus H(b) = V$? Suppose I have the values $a$, $b$, and $V = H(a) \oplus H(b)$ with inputs $a \neq b$ and $H$ being SHA-224. None of these values are a secret.
How secure is it to assume that no other possible values $a'$ and $b'$ (except the case of $a'=b$ and $b'=a$) can be generated that result in the same $V = H(a') \oplus H(b')$?

Are there recommended procedures to combine two hashes into a single value and meet the following properties:


$V$ has same (or nearly same) size as each of both input hashes
Any single unknown value ($V$, $H(a)$, or $H(b)$) can easily be deduced from two known values.
Cryptographically hard to obtain different pre-images $a'$ and $b'$ with same $V$
$ Pr(H(a) \oplus H(b) = V)$ is independent of $V$ For a good hash, as pointed out in the comments. Pick your input space to be the output space of SHA-224 so with probability $1/2$ (1) holds.

The range of $H$ is a group under $\oplus$. So (2) holds. 

3 won't hold by the same group property. Another $2^{112}$ trials will likely yield $a',b'$ satisfying (3) with probability $1/2$.