Matching preamp inputs.

If you can solder, you could build a fixed attenuation network (one for each channel) either into an interconnect cable to be used with the tuner or inside the tuner. At a guess, you might try an 8K ohm resistor in series followed by a 2K ohm resistor to ground. You could try this just by holding the resistors in one of the tuner's RCA jacks and touching them appropriately to the pin and shell of an IC going to the preamp. Or solder together a little external network with RCA jacks. Much cheaper than buying a passive preamp, and it will sound better too, if you get it right.

Your DIY cable might not be a great IC, but I take it that you don't have much quality to lose in your FM sound.

As did my old NAD 1155...

You can also look for an Onkyo Integra T4017, T4087, or T9090 tuner. They all have a variable output adjustment knob on the back.

That is probably why you notice the difference in the knob's action with the two components. Lots of preamp manufacturers will calibrate the level control to have a coarser adjustment action at the bottom of the useable range, and give it finer control as you get into the heart of its range. Check your preamp manual, it might confirm this (I'll go out on a limb and guess that you own a tube preamp - these usually feature more gain than is needed in most systems, hence the lowish volume settings). Ways to rectify this situation are probably few. Some tuners (and DAC's) have variable output controls - if yours does, you might be able equalize things a bit here. Failing that, the easiest thing to do would be to pad down the output of the tuner with an external attenuator. Sorry, but I don't enough about those to give you specific advice on what to get, but if no one on the forum steps up, somebody like Michael Percy Audio might be able to help if your local dealer can't. Good luck!

The tuner has the higher output. Generally the volume knob is between six- and seven o'clock when I am listening to it. With the DAC, I am at 9 o'clock and beyond.

Which source component has the higher output? In other words, is the tuner at a typical volume setting occupying a range on your preamp's volume knob above or below the range you use for the DAC?