The thought of a long open door of grace and the church age soon closing is an amazing thing to take in and yet I totally agree with you that we are on the verge of that. One thing that I love about it though is that even though God may have a set number of "fullness" of gentiles that make up the church and yet I think God always is willing and looking for "just one more, anybody, anybody..." until He has to just close the door and then is that finality you spoke of. One amazing indicator of this is the way that God divides mankind into 1/3 and 2/3.
 
Zechariah 13:

 8.  And it shall come to pass, that in all the land, saith the Lord, two parts therein shall be cut off and die; but the third shall be left therein.
 9.  And I will bring the third part through the fire, and will refine them as silver is refined, and will try them as gold is tried: they shall call on my name, and I will hear them: I will say, It is my people: and they shall say, The Lord is my God.
 
David Flynn did some amazing exposes on the significance of one third of a whole shown as 33 & 1/3 or 33.3333333333333 with as many 3s at the end as you want to include going off the page. This to me is God's way of saying that a number is fixed and yet there is room for just one more if someone wants to get in before it is too late. The reason for the 1/3 vs. 2/3 ratio seems to come from the number of angels that fell with Lucifer and God's plan to replace the hole left in heaven where they once dwelt. Jesus said "In my Father's house ARE many mansions, I go to prepare a place for you." He spoke as though the mansions were there already and uninhabited and Jesus wants to fill them up but they were not yet prepared for mankind and I think that is because they were angel's houses that needed something "remodeled" about hem to make them prepared for humans instead of angels.
 
What a drama this is and it is so exciting that we are about to enter into a "way that we have not passed heretofore..."
 
Joshua 3:
 2.  And it came to pass after three days, that the officers went through the host;
 3.  And they commanded the people, saying, When ye see the ark of the covenant of the Lord your God, and the priests the Levites bearing it, then ye shall remove from your place, and go after it.
 4.  Yet there shall be a space between you and it, about two thousand cubits by measure: come not near unto it, that ye may know the way by which ye must go: for ye have not passed this way heretofore.
 5.  And Joshua said unto the people, Sanctify yourselves: for to morrow the Lord will do wonders among you.
 
What if that is how we are instructed too? If we put in Jesus' name in place of the ark of the covenant? The priests and Levites could represent the cloud of witnesses that will come with Jesus to get us. REMOVE FROM YOUR PLACE AND GO AFTER HIM. Maybe there is a meaning of the "about two thousand cubits" to represent about two thousand years between the first coming and the second coming so that we might know the way that we must go...
 
John 14:
 1.  Let not your heart be troubled: ye believe in God, believe also in me.
 2.  In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you.
 3.  And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also.
 4.  And whither I go ye know, and the way ye know.
 5.  Thomas saith unto him, Lord, we know not whither thou goest; and how can we know the way?
 6.  Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.