If people be able to run homebrew code without any exploit or modchip, then no one ever would need any exploit or modchip in the first place. :]
For Slims with dead ODD the best will be... You know the answer!

Waiting for sd2psx. If You are not patient or want risk and have no friends with hacked PS2, You can buy Memory Card with FMCB but You risking that this card be shitty quality or not covering up Your MG region.
For FAT, the best would be buying Network Adaptor, any. And write there FHDB (or whatever) on PC.