Optimal FEC option for extremely low SNR situation
The one I am considering implementing is an LDPC as outer code and a Turbocode as inner code, with an interleaver in between.

I have not seen any implementation of LDPC and Turbo Codes concatenation yet. There is probably a reason no one tried (which I don't know). The first limitation I see is the fact that decoders need soft-decision inputs in order to be optimum or close to theory. Building an LDPC or Turbo decoder with soft outputs is an effort (COST IPs deliver hard bits on outputs).
Inner-Outer coders topologies were used for technological reasons. At the beginning of communication systems main coders/decoders that were possible to implement (no IC technology limitations) were Convolutional Codes and Reed-Solomon. The decoding gain of each was not enough, so they were combined.
Then arrived Turbo Codes (in the 90's - I was a child) allowing more decoding gain in a single decoder than CC+RS. After then, in the 2000's arrived DVB-S2 and LDPC's. The reason why LDPC is combined with BCH is that there is an error floor. BCH is there to correct those last single errors LDPC cannot correct.

How do these codes perform against burst errors?

Interleaving is really to investigate case by case and depends on your channel. If you find that a burst of errors which can be to much to be corrected in a frame could happen, then interleave several frames is a possible approach.

Would any other combination of codes reduce the necessary Eb/No in order to achieve relatively low (&lt;1e-04) BER?

I think you should be able to pick a single code. The choice is up to your link budget. Finding the code for a given architecture is another story important to consider!
There is a good document that gives an overview of codes used in space communications. Look for CCSDS 130.1-G-3. Figure 3-3 shows Shannon limits, Figure 3-5 some codes comparisons and Figure 7-10 shows Turbo Codes performances.
Also this website has an interactive FEC comparator: https://aff3ct.github.io/comparator.html
Whatever the code you choose to go to the lowest SNR or EbN0, you have to keep in mind how your demodulator is going to behave to lock the low signal. A 0 dB EbN0 LDPC 1/2 BPSK channel can be so &quot;noisy&quot; that some demodulators are not able to lock on it