Increasing gain for your vinyl front end when pre-amp doesn't quite have enough juice

higher output cartridge, assuming your preamp has no adjustability and you have no interest in adding a phono pre.

Love my cart (nagaoka MP-150 I spent a long time researching and trying different carts already) and love my current phono-pre and not interested in spending more than $150 to 'fix' the issue. Between upping the gain on the mani or buying a headphones amp, what would you choose?

At 4.5mV output on your MP-150, you’ll likely be running way to close to the overload margins of a phono stage running at 59 dB - especially a budget phono like the Mani. So in your case, yes adding a headphone amp with a net gain of around say 10-20 dB (careful to find an optimal volume position for whatever you choose) and running the phono at a lower gain would be much more optimal. But it’s still less optimal than just running a single preamp with a good gain structure for your system.

Doesn't your Mani have a 48 dB setting? that should be optimal for your MP-150. If your system is lacking gain at that setting, then ideally you need either more gain in your preamp, more gain in the amp, or more sensitive speakers. 

Up the gain. For when you really need the volume.

The other idea, putting a very low voltage and RIAA equalized cartridge signal into a device designed for line voltage, not to mention adding another interconnect to screw things up, and I'm not even gonna start on grounding issues this mess might cause. You think a little white noise is a problem? You will just have try the headphone amp to appreciate the awfulness of that one. All those scores of step up transformers? The complete lack of headphone amps marketed as step up transformers? Think about it.

What cartridge are you using? What is it's output voltage?
From your post, I am not quite certain what you are using now, except it's a Schiit Mani.  If at least I got that right, is the Mani a phono-only unit or does it include a linestage, which is to say, can you plug your CDP or TV into it as well, which would indicate it has a line level input?  If there is a built-in linestage, when you say the max gain is 59db (an odd number for a manufacturer to state), I assume you refer to total gain, phono stage plus linestage.  Yes? 

Once I get the facts straight, I can try to help.  We also need to know what amplifier and speakers you are using, and if possible the input sensitivity of the amplifier. (Defined as the magnitude of the input signal voltage required to drive the amplifier to its full output.)  But for now, if you are asking about the wisdom of driving another separate linestage with the output from the linestage already built into the Schiit, the answer is "not a good idea".

By the way, what is so terrible about a 70db S/N ratio?  For vinyl, that shouldn't be too obtrusive.