Transformers that can handle larger DC current are larger and thus usually more expensive.
I don't think the circuit will word this way anyway, without a relay to disconnect the line, when not in use. Many systems use the DC current to check if the line is in use. So I would consider a completely different circuit, more a an opto-coupler and the transistor circuit on the line side.
Can you draw a quick sketch of the circuit you have in mind?
The current is ~25ma so should be fine power dissipation wise. I do use a relay, the 0 ohm resistor in the schema represents the relay in closed state for simulation purposes.
I did a quick experiment, loading the secondary with 40ma (secondary in a series with a resistor and a DC power supply) and measuring the primary output voltage. As the DC current increases the output signals changes but I couldn't see any difference in the FFT analysis [0 -10Khz, magnitude in DB)
Voltage with no primary DC current:

voltage with ~40ma primary DC current:

Also tried to actually DTMF dialing and it works like a charm, even though the MCU generates a square wave.