HMAC construction based on the combination of two hash functions
This is proabably a bad idea.

There are several results that indicate there are problems with this design:


While $\oplus$ preserves the PRF property, it is not a robust combiner: it requires that $H_1$ and $H_2$ are independent to guarantee the PRF property is preserved.
i.e. consider what happens to your design if $H_2$ is defined as $H_2(2 \parallel data) = H_1(1 \parallel data)$ 
Boneh06 and Pietrzak07 proved a lower bound on the size for collision resistance preserving combiners, showing that they can't be significantly, i.e. $\theta(log_b)$, smaller than the concatenated size of both hash functions. These papers don't seem to directly address $HMAC$ style key data, but they appear to be quite general results.
Mittelbach13 removed the concatenated size limit for collision resistance preserving combiners, but at the cost of significant time complexity (well beyond the $Comb_{4P}$ combiner introduced in Lehman10 and the combiner you have described) and specific restrictions on the hash functions and the proof.
Part of your motivation for this design appears to be the complexity and expense of the $Comb_{4P}$ combiner, but aside from output size (2 x for $Comb_{4P}$) the schemes appear similar.
i.e. assuming hash functions like SHA-256, with a $block size = 2 \times  output size$, $Comb_{4P}$ requires hashing $M$ with both $H_1$ and $H_2$, followed by 4 further hash blocks and 5 $\oplus$s. With a similar instantiation your design appears to hash $M$ with both $H_1$ and $H_2$, followed by 6 further hash blocks and 1 $\oplus$s.


I'm still trying to get my head round all this, so I could be a little off-base with some of these, but in general this doesn't appear to be an area where easy shortcuts can be taken.

I'm not quite sure what to make of the $HMAC_{H0}(k_0,m) \oplus HMAC_{H1}(k_1,m)$ construction described by Ricky Demer - it looks like it would preserve the PRF properties well, but on the surface it seems to violate the Boneh result on the lower bound for a combiner that preserves collision resistance.