Driving terminated controlled impedance trace single ended

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The resistor won’t damp the signal when it comes back in my opinion but you can try using parallel resistance.

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I don't believe that you have seriously studied transmission line termination schemes. It turns out, that for termination of I/O standards like LVTTL or CMOS, that require to achieve a full voltage swing at the receiver side, series source termination as suggested by gj_leeson is the perfect solution for most point-to-point connections. With correctly adjusted series resistor, it achieves almost reflection free waveforms. A small, usually neglectable deviation from ideal behaviour is caused by the input capacitance of receiver.

It should be also noted, that the 4 mA I/O specification does not mean absolute maximum current. It's the maximum static current to keep the specified output level of the respective IO-standard. In so far it applies to parallel load R termination, but not e.g. to RC load termination or series R termination.

As the main disadvantage of series source termination, it's not suited for tapped transmission lines, because the intended square waveform is only achieved at the transmission line end.