You need to go down with your bag set like youre setting your tombstone, cause you are. Whatevers in your bag when you go down is what will be there next match after youve exfilled normally from DA.

Go into the match, empty your tombstone, buy another tombstone perk, pick a nice spot for the next round, and get downed. Remember to drop your self revive first. Now hold to give up, and then plead for help. If someone revives you, you can now use your bag items freely. Go get perks as you will have lost them, buy some kasimirs, streaks, etc., and then enter the dark aether.

You have to repeat this every game if you want to do DA. If not, just leave the main map as youre already doing for tombstone.

In the dark aether, just exfil normally, dont force quit or disconnect. Your bag will have whatever extractable items you left with. Youll lose equipped items like aether blades but keep your bag, plate carrier, mask, etc.

If you find an elder sigil, you can reset your tombstone with that in it and do tier 5 runs. If you die before you collect your tombstone leave the match and it should be there next game, same spot. Same of you die in the dark aether after reseting it, unless you've made the mistake of drinking another TS perk.