Spell-like abilities count as the spell they are like for the purpose of prerequisites. And invocations that work like a particular spell, even though they have a different name, arguably also count as that spell.

But they never count as “a spell,” or collectively as “spells.” They can count as a particular spell called out by name in a prerequisite, but not as the general concept of spell. Something asking for black tentacles could probably be fulfilled with chilling tentacles, and definitely with a spell-like ability of black tentacles. But a requirement calling for “a spell” (or “ability to cast Xth-level spells”) isn’t going to accept an invocation or spell-like ability. Complete Arcane is quite explicit about this.

And moreover, spellblast and greatreach blast are not requirements, they are abilities. It’s unclear if any of the above would apply to them anyway.

So no, you cannot do this. Those class features require spells. Marrying spells to invocations, after all, is the entire point of eldritch theurge.

Spell-like abilities count as the spell they are like for the purpose of prerequisites. And invocations that work like a particular spell, even though they have a different name, arguably also count as that spell.

But they never count as “a spell,” or collectively as “spells.” They can count as a particular spell called out by name in a prerequisite, but not as the general concept of spell. Something asking for black tentacles could probably be fulfilled with chilling tentacles, and definitely with a spell-like ability of black tentacles. But a requirement calling for “a spell” (or “ability to cast Xth-level spells”) isn’t going to accept an invocation or spell-like ability. Complete Arcane is quite explicit about this, stating that

requirements for feats and prestige classes based on specific levels of spells cast (“Able to cast 3rd-level arcane spells,” for example) cannot be met by spell-like abilities or invocations—not even by spell-like abilities or invocations that allow a character to use a specific arcane spell of the appropriate level or higher.

^{(Chapter Three, Prestige Classes, Invocations and Spell-like Abilities, pg. 72)}

after a lengthy fluff explanation of why the skills used for spell-like abilities and invocations are not the same as those necessary for spellcasting.

And moreover, spellblast and greatreach blast are not requirements, they are abilities. It’s unclear if any of the above would apply to them anyway. By default, with nothing identifying spell-like abilities as equivalent to spells (for this purpose, anyway), they would not be.

So no, you cannot do this. Those class features require spells. Marrying spells to invocations, after all, is the entire point of eldritch theurge.