Question: Is it still considered an infinitive phrase when there is and adjective between "to" and the transitive verb? i.e. to further push

Answer: Yes. The infinitive in your example is "to push." And I have to disagree about others' opinions of split infinitives. There NEVER was a rule banning them. They are and have always been acceptable. Some time ago, someone knowing little about English, decided that since Latin infinitives couldn't be split (ha! Latin infinitives are one word), that English infinitives couldn't be split. Put the modifier where it has the most impact without creating confusion. Thus "To boldly go" is perfectly fine English -- and a very effective use of a "split infinitive."
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