I have been running into the same problem quite often lately. I end up blinded down to desperation and eliminated. I keep going an hour or more with no face cards. Money bubble is about 10% in most tournaments and I end up getting to a shove with ATC because I have 4BB around the time there is 15% of the field left.

Any suggestions for playing with no face cards, and making it just about 5% further?

You are waiting WAY to long to shove all-in. Try waiting until late position and shove allin with about 10-12 BB left. Your stack will be much more scary that someone with 3-5BB and you will have a greater chance of just picking up the blinds. You dont need face cards for this. you could even do it with 27o if you needed to. Sometimes any ace will do or a connector. You have a little less than 50% chance to hit one of your cards.

Just remember that it wont work all the time. Sometimes you'll get called with a better hand and you'll lose earlier on but other times you'll hit and double up and make it even further into the money.

Good luck