Obstruction after the 3rd out called?

Obstruction can only occur if there is a runner (or batter in FED). Once the B/R is out, he isn't a runner and can not be obstructed. On the other hand, it doesn't take physical contact to have obstruction, and it seems possible that the B/R was slowed in his approach to first base by F3. If so, the obstruction occurred before the out. In that case he likely would be awarded first base.

I observed a D3 college game with somewhat of a similar situation...

Batter hit a ground ball to F3 who as he fields it waves off F1 who is racing the batter to first to take the throw. F1 doesn't doesn't stop running and crosses in front of the runner (no contact). Meanwhile, F3 had just stepped across the bag got an Out call from BU. Coach came running out of the dugout asking for the umpires to get together on that one. PU and BU conferred and OBS was call on F1. BR was awarded 1st.

It appears F1 had perhaps slowed the runner in his approach to first in the same way that F3 might have slowed the runner in the OP?

If you think the fielder caused the runner to slow or alter his approach to the base and allowed the other fielder to make the out, then certainly you can call the obstruction. However, you are going to have a tough sell so it needs to be a good call. It sounds like in the OP that was not the case. The way it was worded it sounded like an out then an obstruction a step or so away from the base. In the second play it did sound like an obstruction. This is one of those that you get the big bucks for.