You will eventually get time warnings on every turn because no time gets added back during opponents moves or during your own if you are finally able to make some plays. Perhaps a small time addition of 5-10 sec. would be helpful every time you pick up cards and then later place a set or a run on the table. If your opp is playing a lot of cards it might be nice to get some time to evaluate how you can use all of their plays so maybe a small time addition at the start of the next player's turn or some added time (10-30sec.) during an opponents 1+ minutes of taking and playing cards.
I have run low in time in other games, but they usually give you a bit of a time bump at the start of your turn. This game may require a slightly more substantial bump due to the nature of the game.