Actually, TML, SS has not been replaced, and is a valid part of 3.5. WotC said (my citation-fu is weak, but bear with me) that any 3.0 material that is not updated with a new version (feats, spells, items, classes, as well as entire books) are valid 3.5 rules. However, nothing I've seen says that acquired templates are not part of your race, and you've presented an example of an instance where it is.
SorO:
... Races of the Dragon explicitly lists templated creatures as races: "Races presented in this book that have the dragonblood subtype include dragonborn, spellscale, kobold, and draconic creatures." Or, for that matter, ...
Four paragraphs to say: I don't know how to get Conjure Living Spell to twice a day... Also you know there is a difference between Inherited (half-dragon) and Acquired (mistling) right?
SorO, dragonborn are an acquired template, and are listed as a race. TML already stated this. What would SLAs granted by a template be, if not racial SLAs? TML also already stated that magic in the blood is how he's getting more than one use of CLS. You can make arguments that there are reasons that mistlings don't qualify for MitB, but putting the words 'I don't know how...' in his mouth is disingenuous.
Speaking of dude, only a creature is affected with the normal effect of the Spell and it doesn't even imply the spell is recast on each strike how is that working for you?
This is indeed the crux of the problem with a CLS living spell; neither the slam nor the engulf recast the spell, and the spell effect does nothing to creatures, which are the only things the ooze can target with a slam or engulf. My worries about powering the CLS are but a red herring. As long as the mistling can get 2+ uses of CLS, it can make a CLS living spell, but even if that ooze gets SLAs, it can't activate CLS in any meaningful way.