Hi Robusttheologian, lets go over your assertions one by one.
1) I say Calvinism is both irrational and unbiblical, not one or the other. So you start with a mischaracterization.
2) Scripture does not teach total spiritual inability of all fallen people at all times.
a)Gen. 2:16-17 indicates Adam had a choice and was not compelled by Total Spiritual Inability.
b) John 6:44 says you must first be drawn before you can come to Jesus. It does not say fallen people cannot be drawn.
c) Romans 3:10-12 does not say "at all times." That is added by Calvinist interpretation. But the passage can be understood to be part of Paul's proof that all are under sin, because we are not righteous, when we sin, we do not understand the penalty when we sin, and we are not seeking God when we sin. Thus the quote proves that we all sin.
Now lets turn the tables, and you address my verses: Matthew 23:13 where fallen unregenerate men are "entering heaven" thus at that point in time seeking God, yet are blocked by false teachers. This demonstrates that some men have some ability to seek God without irresistible grace alteration. Thus they have limited spiritual ability, making total spiritual inability as affecting all fallen people at all times unbiblical.